Home » MP Board Class 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 Solution

MP Board Class 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 Solution

In this article, we will share MP Board Class 10th Maths Book Solutions Pair of Linear Equations in Two Variables Exercise 3.1 Pdf solution file.

MP Board Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 Solution

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.

Solution:
At present: Let Aftab’s age = x years
His daughter’s age = y years
Seven years ago : Aftab’s age = (x – 7) years
His daughter’s age = (y – 7)years
According to the condition,
[Aftab’s age] = 7[His daughter’s age]
⇒ [x – 7] = 7[y – 7] = x – 7 = 7y – 49
⇒ x – 7y – 7 + 49 = 0 ⇒ x – 7y + 42 = 0 …. (1)
After three years : Aftab’s age = (x + 3) years
His daughter’s age = (y + 3) years
According to the condition,
[Aftab’s age] = 3[His daughter’s age]
⇒ [x + 3] = 3[y + 3]
⇒ x + 3 = 3y + 9 ⇒ x — 3y + 3 — 9 = 0
⇒ x — 3y – 6 = 0 …. (2)
Graphical representation of equation (1) and (2): From equation (1), we have :

Exercise  3.1 Question 1
Maths Exercise 3.1
10th Exercise 3.1

MP Board Class 10th Maths Exercise 3.1 Solution

Question 2.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.

Solution:
Let the cost of a bat = ₹ x
and the cost of a ball = ₹ y
Cost of 3 bats = ₹ 3x
and cost of 6 balls = ₹ 6y
Again, cost of 1 bat = ₹ x
and cost of 3 balls = ₹ 3y
Algebraic representation:
Cost of 3 bats + Cost of 6 balls = ₹ 3900
⇒ 3x + 6y = 3900 ⇒ x + 2y = 1300 …. (1)
Also, cost of 1 bat + cost of 3 balls = ₹ 1300
⇒ x + 3y = 1300 …. (2)
Thus, (1) and (2) are the algebraic representations of the given situation.
Geometrical representation:
We have for equation (1),

We can also see from the obtained graph that the straight lines representing the two equations intersect at (1300, 0).

10th Maths Exercise 3.1 Solutions

MP Board Solutions

Question 3.
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically.

Solution:
Let the cost of 1 kg of apples = ₹ x
And the cost of 1 kg of grapes = ₹ y
Algebraic representation:
2x + y = 160 … (1)
and 4x + 2y = 300
⇒ 2x + y = 150 … (2)
Geometrical representation:
We have, for equation (1),

10th Exercise 3.1

The straight lines l1 and l2 are the geometrical representations of the equations (1) and (2) respectively. The lines are parallel.

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