Question

x = a, y = b is the solution of the pair of equations 3x + y = 10 and x – y = 2, then (a, b) is equal to ______.

Options

• (3, 1)

• (1, 3)

• (2, 5)

• (5, 2)

Answer 1

x = a, y = b is the solution of the pair of equations 3x + y = 10 and x – y = 2, then (a, b) is equal to (3, 1).

Explanation:

Given the pair of equations:

1. 3x + y = 10
2. x – y = 2

Let the solution be (a, b),

So x = a and y = b.

From equation (2):

x – y = 2

⇒ a – b = 2   ...(i)

From equation (1):

3x + y = 10

⇒ 3a + b = 10   ...(ii)

Add (i) and (ii):

(a – b) + (3a + b) = 2 + 10

⇒ a – b + 3a + b = 12

⇒ 4a = 12

⇒ a = 3

Substitute a = 3 into (i):

3 – b = 2

⇒ b = 1

So, the solution is (a, b) = (3, 1).