Ifx + 2y = 8 and - 2x + 3y = 5, then what is the value of 2x + 3y?

13

Step-by-step explanation:

Given the 2 equations

x + 2y = 8 → (1)

- 2x + 3y = 5 → (2)

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

x = 8 - 2y → (3)

Substitute x = 8 - 2y into (2)

- 2 (8 - 2y) + 3y = 5 ← distribute and simplify left side

- 16 + 4y + 3y = 5

- 16 + 7y = 5 (add 16 to both sides)

7y = 21 (divide both sides by 7)

y = 3

Substitute y = 3 in (3) for corresponding value of x

x = 8 - 2 (3) = 8 - 6 = 2

Thus x = 2 and y = 3

2x + 3y = 2 (2) + 3 (3) = 4 + 9 = 13