NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1

NCERT Solutions Class 10 Maths 
Chapter – 3 (Pair of Linear Equations in Two Variables) 

The NCERT Solutions in English Language for Class 10 Mathematics Chapter – 3 Pair of Linear Equations in Two Variables Exercise 3.1 has been provided here to help the students in solving the questions from this exercise.

Chapter : 3 Pair of Linear Equations in Two Variables

• NCERT Class 10 Maths Solution Ex – 3.2
• NCERT Class 10 Maths Solution Ex – 3.3
• NCERT Class 10 Maths Solution Ex – 3.4
• NCERT Class 10 Maths Solution Ex – 3.5
• NCERT Class 10 Maths Solution Ex – 3.6
• NCERT Class 10 Maths Solution Ex – 3.7

Exercise – 3.1 

1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Solutions –
Let the present age of Aftab be ‘x’.
And, the present age of his daughter be ‘y’.
Now, we can write, seven years ago,
Age of Aftab = x – 7
Age of his daughter = y – 7
According to the question,
x − 7 = 7(y − 7)
x − 7 = 7y − 49
x − 7y = −42         —————- (i)
Also, three years from now or after three years,
Age of Aftab will become = x + 3.
Age of his daughter will become = y + 3
According to the situation given,
x + 3 = 3(y + 3)
x + 3 = 3y + 9
x − 3y = 6     —————– (ii)
Subtracting equation (i) from equation (ii) we have
(x − 3y) − (x − 7y) = 6 − (−42)
−3y + 7y = 6 + 42
4y = 48
y = 12
The algebraic equation is represented by
x − 7y = −42
x − 3y = 6
For, x − 7y = −42
x = −42+7y
The solution table is

For,  x − 3y = 6
x = 6 + 3y
The solution table is

The graphical representation is:

2. The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.
Solutions – Let us assume that the cost of a bat be Rs ‘x’
And, the cost of a ball be Rs ‘y’
According to the question, the algebraic representation is
3x + 6y = 3900  ————– (i)
x + 3y = 1300  ————– (ii)
For 3x + 6y = 3900
x + 2y = 1300
x = 1300 – 2y
The solution table is

For, x + 3y = 1300
x = 1300 – 3y
The solution table is

The graphical representation is as follows.

3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Represent the situation algebraically and geometrically.
Solutions – Let the cost of 1 kg of apples be Rs. ‘x’
And, cost of 1 kg of grapes be Rs. ‘y’
According to the question, the algebraic representation is
2x + y = 160            ————- (i)
4x + 2y = 300        ————- (ii)
For, 2x + y = 160
y = 160 − 2x
the solution table is;

For 4x + 2y = 300
y = (300 – 4x)/2,
y = 150 – 2x
the solution table is;

The graphical representation is as follows;

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