{"id":4257,"date":"2023-02-05T05:44:41","date_gmt":"2023-02-05T05:44:41","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4257"},"modified":"2023-02-05T05:46:06","modified_gmt":"2023-02-05T05:46:06","slug":"ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-3\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.3"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 4 (Linear Equations in Two Variables)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 4 Linear Equations in Two Variables <\/strong>Exercise 4.3 has been provided here to help the students in solving the questions from this exercise.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 4: Linear Equations in Two Variables<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.4<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 4.3\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. Draw the graph of each of the following linear equations in two variables:<br \/>\n<\/strong><strong>(i) x + y = 4<br \/>\n<\/strong><strong>(ii) x \u2013 y = 2<br \/>\n(iii) y = 3x<br \/>\n(iv) 3 = 2x + y<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong><strong>(i) x + y = 4<br \/>\n<\/strong>\u21d2 y = 4 \u2013 x<br \/>\nIf we have x = 0, then y = 4 \u2013 0 = 4<br \/>\nx = 1, then y =4 \u2013 1 = 3<br \/>\nx = 2, then y = 4 \u2013 2 = 2<br \/>\n\u2234 We get the following table:<br \/>\n<\/span><\/p>\n<table style=\"width: 40%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">1<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">4<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">3<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4275\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1a.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"577\" height=\"373\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1a.png 740w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1a-300x194.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1a-480x310.png 480w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii) x \u2013 y = 2<br \/>\n<\/strong>\u21d2 y = x &#8211; 2<br \/>\nIf we have x = 0, then y = 0 \u2013 2 = -2<br \/>\nx = 2, then y = 2 \u2013 2 = 0<br \/>\n\u2234 We get the following table:<br \/>\n<\/span><\/p>\n<table style=\"width: 40%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">-2<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4276\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1b.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"235\" height=\"295\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iii) y = 3x<br \/>\n<\/strong>If we have x = 0, then y = 0<br \/>\nx = 1, then y = 3<br \/>\n\u2234 We get the following table:<br \/>\n<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 48px;\">\n<tbody>\n<tr>\n<td style=\"width: 19.0938px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 7.95312px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 10.9531px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.0938px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 7.95312px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 10.9531px; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">3<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4277\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans1c.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"268\" height=\"328\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans1c.png 332w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans1c-245x300.png 245w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iv) 3 = 2x + y<br \/>\n<\/strong>\u21d2 y = 3 &#8211; 2x<br \/>\nIf we have x = 0, then y = 3 \u2013 0 = 3<br \/>\nx = 1, then y = 3 \u2013 2 = 1<br \/>\n\u2234 We get the following table:<br \/>\n<\/span><\/p>\n<table style=\"width: 40%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">3<\/span><\/td>\n<td style=\"width: 25%; text-align: center;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4274\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1d.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"267\" height=\"320\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1d.png 267w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q1d-250x300.png 250w\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>2. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>Point (2, 14) at which lines passing through.<br \/>\nWe can think of framing equations that could satisfy the given point (2, 14) on the line.<br \/>\nIt can be observed that point (2, 14) satisfies the equation 7x &#8211; y = 0 and x &#8211; y + 12 = 0.<br \/>\nTherefore, 7x &#8211; y = 0 and x &#8211; y + 12 = 0 are two lines passing through point (2, 14).<br \/>\nSince we know infinite lines can pass through a single point, therefore there are infinite more lines passing through the given point.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>3. If the point (3, 4) lies on the graph of the equation 3y = ax+7, find the value of a. <\/strong><br \/>\n<strong>Answer &#8211;\u00a0<\/strong>The given equation is 3y = ax + 7<br \/>\nAccording to the question, x = 3 and y = 4<br \/>\nNow, substituting the values of x and y in the equation 3y = ax + 7,<br \/>\nWe get,<br \/>\n(3 \u00d7 4) = (a \u00d7 3) + 7<br \/>\n\u21d2 12 = 3a + 7<br \/>\n\u21d2 3a = 12 \u2013 7<br \/>\n\u21d2 3a = 5<br \/>\n\u21d2 a = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{3}\" alt=\"\\frac{5}{3}\" align=\"absmiddle\" \/><br \/>\nThe value of a, if the point (3, 4) lies on the graph of the equation 3y = ax+7 is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{3}\" alt=\"\\frac{5}{3}\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>4. The taxi fare in a city is as follows: For the first kilometre, the fare is\u00a0<\/strong>\u20b9<strong>8, and for the subsequent distance, it is\u00a0<\/strong>\u20b9<strong>5 per km. Taking the distance covered as x km and total fare as\u00a0<\/strong>\u20b9<strong>\u00a0y, write a linear equation for this information, and draw its graph.<br \/>\n<\/strong><strong>Answer &#8211;<br \/>\n<\/strong>Total distance covered = x<br \/>\nTotal fare = y<br \/>\nFare for the first kilometre = 8 per km<br \/>\nFare after the first 1 km = 5 per km<br \/>\nIf x is the total distance, then the distance after one km = (x &#8211; 1)km<br \/>\ni.e., fare after the first km = 5(x &#8211; 1)<br \/>\nAccording to the question,<br \/>\nThe total fare = Fare of first km + fare after the first km<br \/>\ny = 8 + 5(x &#8211; 1)<br \/>\ny = 8 + 5(x &#8211; 1)<br \/>\ny = 8 + 5x \u2013 5<br \/>\ny = 5x + 3<br \/>\nSolving the equation,<br \/>\n<strong>When x = 0<\/strong>,<br \/>\ny = 5x + 3<br \/>\ny = 5\u00d70+3<br \/>\ny = 3<br \/>\n<strong>When y = 0,<br \/>\n<\/strong>y = 5x + 3<br \/>\no = 5x+3<br \/>\n5x = -3<br \/>\nx = -3\/5<br \/>\n<\/span><\/p>\n<table style=\"width: 40%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">x<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">&#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\" alt=\"\\frac{3}{5}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">y<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">3<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4278\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans4.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"355\" height=\"444\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans4.png 355w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans4-240x300.png 240w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.<\/strong><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 120px;\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">For Fig. 4. 6<\/span><\/strong><\/span><\/td>\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">For Fig. 4. 7<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i) y = x<\/span><\/td>\n<td style=\"width: 50%; height: 24px;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">(i) y = x + 2\u00a0 \u00a0<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 50%; height: 24px;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">(ii) x + y = 0<br \/>\n<\/span><\/td>\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(ii) y = x \u2013 2<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 50%; height: 24px;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">(iii) y = 2x<br \/>\n<\/span><\/td>\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iii) y = \u2013x + 2<\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 50%; height: 24px;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">(iv) 2+3y = 7x<br \/>\n<\/span><\/td>\n<td style=\"width: 50%; height: 24px;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iv) x+2y = 6<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4279\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q5.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"716\" height=\"376\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q5.png 838w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q5-300x158.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q5-768x403.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q5-480x252.png 480w\" sizes=\"auto, (max-width: 716px) 100vw, 716px\" \/><br \/>\nAnswer &#8211; <\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">The points given in <strong>figure 4.6<\/strong> are (0, 0), (-1, 1), (1, -1)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Substituting the values for x and y from these points in the equations, we get,<br \/>\n<\/span><strong><span style=\"font-family: georgia, palatino, serif;\">(i) y = x<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 0)<\/strong><br \/>\n\u21d2 0 = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 1)<\/strong><br \/>\n\u21d2 -1 \u2260 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(1, -1)<\/strong><br \/>\n\u21d2 1 \u2260 -1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) x + y = 0<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 0)<\/strong><br \/>\n\u21d2 0 + 0 = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 1)<\/strong><br \/>\n\u21d2 -1 + 1 = 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(1, -1)<\/strong><br \/>\n\u21d2 1 + (-1) =0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iii) y = 2x<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 0)<\/strong><br \/>\n\u21d2 0 = 2\u00d70 = <\/span><span style=\"font-family: georgia, palatino, serif;\">0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 1)<\/strong><br \/>\n\u21d2 1 = 2\u00d7(-1)<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">1 \u2260 -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(1, -1)<\/strong><br \/>\n\u21d2 -1 = 2\u00d71<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">-1 \u2260 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iv) 2 + 3y = 7x<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 0)<\/strong><br \/>\n\u21d2 2 + (3\u00d70) = 7\u00d70<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 2 \u2260 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 1)<\/strong><br \/>\n\u21d2 2 + (3\u00d71) = 7\u00d7-1<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">5 \u2260 -7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(1, -1)<\/strong><br \/>\n\u21d2 2 + (3\u00d7-1) = 7\u00d71<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">-1 \u2260 7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Equation (ii)\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x <\/span><span class=\"mbin\">+ <\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y <\/span><span class=\"mrel\">= <\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span>, satisfies these solutions.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">For Fig. 4. 7<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">The points given in figure 4.7 are (0,2), (2,0), (-1,3)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Substituting the values for x and y from these points in the equations, we get,<br \/>\n<\/span><strong><span style=\"font-family: georgia, palatino, serif;\">(i) y = x + 2<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 2)<\/strong><br \/>\n\u21d2 2 = 0 + 2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">2 = 2 <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(2, 0)<\/strong><br \/>\n\u21d2 0 = 2+2<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">0 \u2260 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 3)<\/strong><br \/>\n\u21d2 3 = -1 + 2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 3 \u2260 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) y = x\u20132<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 2)<\/strong><br \/>\n\u21d2 2 = 0 \u2013 2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 2 \u2260 -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(2, 0)<\/strong><br \/>\n\u21d2 0 = 2\u20132<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 0= 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 3)<\/strong><br \/>\n\u21d2 3 = \u20131\u20132<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 3 \u2260 \u20133\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iii) y = \u2013x + 2<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 2) <\/strong><br \/>\n\u21d2 2 = -0 + 2<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">2 = 2<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(2, 0)<\/strong><br \/>\n\u21d2 0 = -2 + 2<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">0 = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 3)<\/strong><br \/>\n\u21d2 3 = -(-1) + 2<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">3 = 3<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iv) x + 2y = 6<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>(0, 2)<\/strong><br \/>\n\u21d2 0 + (2\u00d72) = 6<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">4 \u2260 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(2, 0)<\/strong><br \/>\n\u21d2 2 + (2\u00d70) = 6<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">2 \u2260 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(-1, 3) <\/strong><br \/>\n\u21d2 -1 + (2\u00d73) = 6<br \/>\n\u21d2 <\/span><span style=\"font-family: georgia, palatino, serif;\">5 \u2260 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>equation not satisfied<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Equation (iii)\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span>\u00a0, satisfies these solutions.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>6. If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also, read from the graph the work done when the distance travelled by the body is<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) 2 units<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) 0 unit<br \/>\n<\/strong><\/span><strong><span style=\"font-family: georgia, palatino, serif;\">Answer &#8211; <\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">We can consider distance traveled by the body and the work done as &#8216;x&#8217; and &#8216;y&#8217; respectively and then apply the direct proportion property.<br \/>\n<\/span>Let the distance traveled and the work done by the body be x and y respectively.<\/span><br \/>\n<span style=\"color: #000000;\">The constant force applied to the body is 5 units.<\/span><br \/>\n<span style=\"color: #000000;\">Work done \u221d distance traveled. <\/span><br \/>\n<span style=\"color: #000000;\">Hence, y \u221d x <\/span><br \/>\n<span style=\"color: #000000;\">y = kx\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-Equation (1)<\/span><br \/>\n<span style=\"color: #000000;\">Where k is the constant force applied on the body, given as 5. Thus, y = 5x.<\/span><br \/>\n<span style=\"color: #000000;\">By substituting different values of x in\u00a0equation\u00a0(1) we get different values for y<\/span><br \/>\n<span style=\"color: #000000;\">When x = 0, y = 0<\/span><br \/>\n<span style=\"color: #000000;\">When x = 2, y = 10<\/span><\/p>\n<table style=\"width: 40%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">y<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000;\">10<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">The graph of the line represented by the given equation is shown below.<\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4270\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q6.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"332\" height=\"648\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q6.png 332w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q6-154x300.png 154w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i)<\/strong> From the graphs, it can be observed that the value of y corresponding to x = 2 is 10 units. This implies that the work done by the body is 10 units when the distance traveled by it is 2 units.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii)<\/strong> From the graphs, it can be observed that the value of y corresponding to x = 0 is 0. This implies that the work done by the body is 0 units when the distance traveled by it is 0 units.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>7. Yamini and Fatima, two students of Class IX of a school, together contributed \u20b9 100 towards the Prime Minister\u2019s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data (You may take their contributions as \u20b9 x and \u20b9 y). Draw the graph of the same.<br \/>\n<\/strong><\/span><strong><span style=\"font-family: georgia, palatino, serif;\">Answer &#8211; <\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">We can assume Yamini and Fatima&#8217;s contributions as \u20b9 x and \u20b9 y respectively, and form a linear equation.<br \/>\n<\/span>Let the amount that Yamini and Fatima have contributed individually be \u20b9 x and \u20b9 y respectively towards the Prime Minister\u2019s Relief Fund.<\/span><br \/>\n<span style=\"color: #000000;\">The total amount contributed by Yamini and Fatima together is = \u20b9 100<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, x + y = 100<\/span><br \/>\n<span style=\"color: #000000;\">On transposing, y = 100 &#8211; x<\/span><br \/>\n<span style=\"color: #000000;\">This is a linear equation in two variables of the form ax + by + c = 0<\/span><br \/>\n<span style=\"color: #000000;\">Let us consider this y = 100 &#8211; x\u00a0 &#8212;&#8212;&#8212;\u00a0 Equation (1)<\/span><br \/>\n<span style=\"color: #000000;\">By substituting different values of x in the\u00a0equation\u00a0(1), we get different values for y<\/span><br \/>\n<span style=\"color: #000000;\">When x = 0, y = 100<\/span><br \/>\n<span style=\"color: #000000;\">When x = 50, y = 50<\/span><br \/>\n<span style=\"color: #000000;\">When x = 100, y = 0<\/span><br \/>\n<span style=\"color: #000000;\">Thus, we have the following table with all the obtained values of x and y:<\/span><\/p>\n<table style=\"width: 50%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">50<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">100<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">50<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">50<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">The graph of the line represented by the given equation is as shown.<\/span><\/p>\n<p><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4280\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans7.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"589\" height=\"578\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans7.png 589w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans7-300x294.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Ans7-480x471.png 480w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Here, variables x and y are representing the amount contributed by Yamini and Fatima respectively and these quantities cannot be negative. Hence, only those values of x and y which are lying in the 1<sup>st<\/sup>\u00a0quadrant are considered.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>8. In countries like USA and Canada, the temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{F&amp;space;=&amp;space;\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;+&amp;space;32}\" alt=\"\\mathbf{F = \\left ( \\frac{9}{5} \\right )C + 32}\" width=\"138\" height=\"44\" align=\"absmiddle\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(i) Draw the graph of the linear equation above using Celsius for the x-axis and Fahrenheit for the y-axis.<br \/>\n<\/span><\/strong><strong><span style=\"font-family: georgia, palatino, serif;\">Answer &#8211; <\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">According to the question,<br \/>\n<\/span><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?F&amp;space;=&amp;space;\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;+&amp;space;32\" alt=\"F = \\left ( \\frac{9}{5} \\right )C + 32\" align=\"absmiddle\" \/> <\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">We get,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">When C = 0, F = 32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">When C = -10 , F = 14<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The points to be plotted are (0, 32), (-10, 14)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4269\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q8.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"476\" height=\"554\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q8.png 476w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-4.3-Q8-258x300.png 258w\" sizes=\"auto, (max-width: 476px) 100vw, 476px\" \/><br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) If the temperature is 30\u00b0C, what is the temperature in Fahrenheit?<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>When C = 30,<br \/>\n<\/span><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?F&amp;space;=&amp;space;\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;+&amp;space;32\" alt=\"F = \\left ( \\frac{9}{5} \\right )C + 32\" width=\"135\" height=\"44\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">F = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9\\times&amp;space;30}{5}\" alt=\"\\frac{9\\times 30}{5}\" align=\"absmiddle\" \/> + 32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (9\u00d76)+32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 54 + 32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 86<sup>o<\/sup>F<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) If the temperature is 95\u00b0F, what is the temperature in Celsius?<\/strong><br \/>\n<strong>Answer &#8211; <\/strong>When F = 95,<br \/>\n<\/span><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?95&amp;space;=&amp;space;\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;+&amp;space;32\" alt=\"95 = \\left ( \\frac{9}{5} \\right )C + 32\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;=&amp;space;95&amp;space;-&amp;space;32\" alt=\"\\left ( \\frac{9}{5} \\right )C = 95 - 32\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;=&amp;space;63\" alt=\"\\left ( \\frac{9}{5} \\right )C = 63\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?C&amp;space;=&amp;space;\\frac{63\\times&amp;space;5}{9}\" alt=\"C = \\frac{63\\times 5}{9}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">=35<sup>o<\/sup>C<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iv) If the temperature is 0\u00b0C, what is the temperature in Fahrenheit, and if the temperature is 0\u00b0F, what is the temperature in Celsius?<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\"><strong>Answer &#8211; <\/strong>When C = 0,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?F&amp;space;=&amp;space;\\left&amp;space;(&amp;space;\\frac{9}{5}&amp;space;\\right&amp;space;)C&amp;space;+&amp;space;32\" alt=\"F = \\left ( \\frac{9}{5} \\right )C + 32\" width=\"135\" height=\"44\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 0 + 32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 32<sup>o<\/sup>F<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">When F = 0,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{5}\" alt=\"\\frac{9}{5}\" align=\"absmiddle\" \/> C + 32<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{5}\" alt=\"\\frac{9}{5}\" align=\"absmiddle\" \/> C = 0 &#8211; 32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{5}\" alt=\"\\frac{9}{5}\" align=\"absmiddle\" \/> C = -32<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32\\times&amp;space;5}{9}\" alt=\"\\frac{-32\\times 5}{9}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= -17.7777<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">=-17.8<sup>o<\/sup>C<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.<br \/>\nAnswer &#8211;\u00a0 <\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">When F = C,<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">C = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{5}\" alt=\"\\frac{9}{5}\" align=\"absmiddle\" \/> C + 32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">C \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{5}\" alt=\"\\frac{9}{5}\" align=\"absmiddle\" \/> C = 32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(5-9)}{5}\" alt=\"\\frac{(5-9)}{5}\" align=\"absmiddle\" \/> C\u00a0=32 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/> C = 32 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">C = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(-32\\times&amp;space;5)}{4}\" alt=\"\\frac{(-32\\times 5)}{4}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u2013 40<sup>o<\/sup>C<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, -40<sup>o<\/sup>\u00a0is the temperature which is numerically the same in both Fahrenheit and Celsius.<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 4 (Linear Equations in Two Variables)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 4 Linear Equations in Two Variables Exercise 4.3 has been provided here to help the students in solving the questions from this exercise. Chapter 4: Linear Equations in Two Variables NCERT [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[707,702,186,708,701,5],"class_list":["post-4257","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-4-linear-equations-in-two-variables-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-4-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.3 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 9 Maths\u00a0Chapter - 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