Question

The solution of the equations x + 2y = 1.5 and 2x + y = 1.5 is

(a) x = 1 and y = 1
(b) x = 1.5 and y = 1.5
(c) x = 0.5 and y = 0.5
(d) none of these

Answer 1

C

Explanation:

Given the 2 equations

x + 2y = 1.5 → (1)

2x + y = 1.5 → (2)

Rearrange (1) expressing x in terms of y by subtracting 2y from both sides

x = 1.5 - 2y → (3)

Substitute x = 1.5 - 2y in (2)

2(1.5 - 2y) + y = 1.5 ← distribute left side

3 - 4y + y = 1.5

3 - 3y = 1.5 ( subtract 3 from both sides )

- 3y = - 1.5 ( divide both sides by - 3 )

y = 0.5

Substitute y = 0.5 into (3) for corresponding value of x

x = 1.5 - (2 × 0.5) = 1.5 - 1 = 0.5

Solution is x = 0.5 and y = 0.5 → C