Question

If 2x + y = 7 and x + 2y = 11, then find the value of x + y.

Answer 1

Given:

2x + y = 7  ...(i)

x + 2y = 11  ...(ii)

Multiply equation (ii) by 2 to make the coefficients of x the same: 

2(x + 2y) = 2(11)

2x + 4y = 22  ...(iii)

Subtract equation (i) from equation (iii)

2x + 4y = 22

2x + y = 7   
3y = 15

y = `15/3`

y = 5

Substitute y = 5 in equation (i)

2x + y = 7

2x + 5 = 7

2x = 7 − 5

2x = 2

x = `2/2`

x = 1

∴ x + y = 1 + 5 = 6