NCERT solution class 10 chapter 3 Pair of Linear Equations in Two Variables exercise 3.1

EXERCISE 3.1

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Introduction - Pair of Linear Equations in Two Variable, CBSE Class 10th Maths

Q 1, Ex 3.1 - Linear Equations - Chapter 3 - Maths Class 10th - NCERT

Page No 44:

Question 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.

Answer:

Let the present age of Aftab be x.
And, present age of his daughter = y
Seven years ago,
Age of Aftab = x − 7
Age of his daughter = y − 7
According to the question,

Three years hence,
Age of Aftab = x + 3
Age of his daughter = y + 3
According to the question,

Therefore, the algebraic representation is

For ,

The solution table is

x	− 7	0	7
y	5	6	7

For ,

The solution table is

x	6	3	0
y	0	− 1	− 2

The graphical representation is as follows.

Q 2, Ex 3.1 - Linear Equations - Chapter 3 - Maths Class 10th - NCERT

Question 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.

Answer 2:

Let the cost of a bat be Rs x.
And, cost of a ball = Rs y
According to the question, the algebraic representation is

$$\begin{gathered} 3x+6y = 3900 \\ x+3y = 1300 \end{gathered}$$
For ,

The solution table is

x	300	100	− 100
y	500	600	700

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

x	1000	700	400
y	100	200	300

The graphical representation is as follows.

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Question 3:

The cost of 2 kg of apples and 1 kg 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.

Answer:

Let the cost of 1 kg of apples be Rs x.
And, cost of 1 kg of grapes = Rs y
According to the question, the algebraic representation is

For ,

The solution table is

x	50	60	70
y	60	40	20

For 4x + 2y = 300,

The solution table is

x	70	80	75
y	10	−10	0

The graphical representation is as follows.

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