CBSE, NCERT Solutions for Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables Exercise 3.1

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:
Present age Aftab =x years and present age of Aftab's daughter's is =y

1st Sititution
7 Years Ago
→  x - 7 = 7(y - 7)
⇒ x -7 = 7y - 49
⇒ x - 7y = - 49 + 7
⇒ x - 7y = - 42

Table:
X 0 - 42 - 35
y 6 0 1



2nd Sititution
3 Years Later
→  x + 3 = 3(y +3 )
⇒ x + 3 = 3y + 9
⇒ x - 3y = 9 - 3
⇒ x - 3y = 6

Table:

X
6
0
9
y
0
- 2
1

The Algebraic equations are :
x - 7y = - 42 and x - 3y = 6
You can also download the free PDF of  Ex 3.1 Class 10 Pair of Linear Equations in Two Variables NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.
Download NCERT Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables PDF
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:



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:
Cost of one kg apples is = x rupees and one kg grapes is = y rupees.


1st Sititution

→  2x + y = 160

Table:

X806040
y04080

2nd Sititution

→  4x + 2y = 300

Table:

X606020
y3070110

The Algebraic Sititutions are 2x + y = 160 and 4x + 2y = 300


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