{"id":4255,"date":"2023-02-05T05:44:34","date_gmt":"2023-02-05T05:44:34","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4255"},"modified":"2023-02-05T05:45:41","modified_gmt":"2023-02-05T05:45:41","slug":"ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-1\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1"},"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 4.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/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-4-2\/\" 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-4-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.3<\/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; 4.1\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.<br \/>\n<\/strong><strong>(Take the cost of a notebook to be \u20b9 x and that of a pen to be \u20b9 y)<br \/>\n<\/strong><strong>Answer &#8211;<\/strong> \u00a0Let the cost of a notebook be = \u20b9 x<br \/>\nLet the cost of a pen be = \u20b9 y<br \/>\nAccording to the condition, we have<br \/>\nCost of a notebook =2 \u00d7 Cost of a pen<br \/>\nx = 2 \u00d7 y<br \/>\nx = 2y<br \/>\nx &#8211; 2y = 0<br \/>\nThus, the required linear equation is x \u2013 2y = 0.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case.<br \/>\n(i) 2x + 3y =\u00a0<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mn\">9.3<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\overline{5}}\" alt=\"\\mathbf{\\overline{5}}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><br \/>\n(ii)\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-7\" class=\"math\"><span id=\"MathJax-Span-8\" class=\"mrow\"><span id=\"MathJax-Span-9\" class=\"mi\">x <\/span><span id=\"MathJax-Span-10\" class=\"mo\">\u2212 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{y}{5}}\" alt=\"\\mathbf{\\frac{y}{5}}\" align=\"absmiddle\" \/> <\/span><span id=\"MathJax-Span-14\" class=\"mo\">\u2212 <\/span><span id=\"MathJax-Span-15\" class=\"mn\">10 <\/span><span id=\"MathJax-Span-16\" class=\"mspace\"><\/span><span id=\"MathJax-Span-17\" class=\"mo\">= <\/span><span id=\"MathJax-Span-18\" class=\"mspace\"><\/span><span id=\"MathJax-Span-19\" class=\"mn\">0<br \/>\n<\/span><\/span><\/span><\/span>(iii) \u2013 2x + 3y = 6<br \/>\n(iv) x = 3y<br \/>\n(v) 2x = -5y<br \/>\n(vi) 3x + 2 = 0<br \/>\n(vii) y \u2013 2 = 0<br \/>\n(viii) 5 = 2x<br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong><strong>(i) 2x + 3y =\u00a0<span class=\"MathJax\" tabindex=\"0\"><span class=\"math\"><span class=\"mrow\"><span class=\"mn\">9.3<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\overline{5}}\" alt=\"\\mathbf{\\overline{5}}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/span><\/span><\/span><\/strong>2x + 3y <span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mo\">\u2212 <\/span><span id=\"MathJax-Span-29\" class=\"mn\">9.<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-20\" class=\"math\"><span id=\"MathJax-Span-21\" class=\"mrow\"><span id=\"MathJax-Span-22\" class=\"mn\">3<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\overline{5}\" alt=\"\\overline{5}\" align=\"absmiddle\" \/> <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>= 0<\/span><br \/>\n<span style=\"color: #000000;\">Comparing it with ax + by +c = 0, <\/span><br \/>\n<span style=\"color: #000000;\">we get a = 2, b = 3 and c= \u2013<span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-33\" class=\"math\"><span id=\"MathJax-Span-34\" class=\"mrow\"><span id=\"MathJax-Span-35\" class=\"mn\">9.<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-20\" class=\"math\"><span id=\"MathJax-Span-21\" class=\"mrow\"><span id=\"MathJax-Span-22\" class=\"mn\">3<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\overline{5}\" alt=\"\\overline{5}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii)\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-7\" class=\"math\"><span id=\"MathJax-Span-8\" class=\"mrow\"><span id=\"MathJax-Span-9\" class=\"mi\">x <\/span><span id=\"MathJax-Span-10\" class=\"mo\">\u2212 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{y}{5}}\" alt=\"\\mathbf{\\frac{y}{5}}\" align=\"absmiddle\" \/> <\/span><span id=\"MathJax-Span-14\" class=\"mo\">\u2212 <\/span><span id=\"MathJax-Span-15\" class=\"mn\">10 <\/span><span id=\"MathJax-Span-16\" class=\"mspace\"><\/span><span id=\"MathJax-Span-17\" class=\"mo\">= <\/span><span id=\"MathJax-Span-18\" class=\"mspace\"><\/span><span id=\"MathJax-Span-19\" class=\"mn\">0<br \/>\n<\/span><\/span><\/span><\/span><\/strong>x &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/>y &#8211; 10= 0<\/span><br \/>\n<span style=\"color: #000000;\">Comparing it with ax + by + c = 0, <\/span><br \/>\n<span style=\"color: #000000;\">we get a =1, b = &#8211;<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/> and c = -10<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) \u20132x + 3y = 6<br \/>\n<\/strong>\u2013 2x + 3y \u2013 6 = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get, a = \u20132, b = 3 and\u00a0c =-6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) x = 3y<br \/>\n<\/strong>x &#8211; 3y = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get a = 1,\u00a0b = -3 and\u00a0c =0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 2x = \u20135y<br \/>\n<\/strong>2x + 5y = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get a = 2,\u00a0b = 5 and\u00a0c = 0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) 3x + 2 = 0<br \/>\n<\/strong>3x + 0y + 2 = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get a = 3, b = 0 and\u00a0c = 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) y \u2013 2 = 0<br \/>\n<\/strong>0x + 1y \u20132 = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get a = 0, b = 1 and c = \u20132<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(viii) 5 = 2x<br \/>\n<\/strong>2x &#8211; 5 = 0<strong><br \/>\n<\/strong>2x + 0y \u2013 5 = 0<br \/>\nComparing it with ax + by + c = 0,<br \/>\nWe get a = 2,\u00a0b = 0 and\u00a0c = -5<\/span><\/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 4.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 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-4255","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 4.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 9 Maths\u00a0Chapter - 4 (Linear Equations 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