Question

Solve the following using the method of substitution:
$\text{2x - 3y = 2, x + 2y = 8}$

• A. x = 6, y = 2
• B. x = 6, y = 4
• C. x = 4, y = 2
• D. x = 6, y = 6

Answer 1

The correct option is C x = 4, y = 2

Given equations are:
2x - 3y = 2-------(1)
x + 2y = 8-------(2)

From (2), we have,
x = 8 - 2y

Substituting this values of x in (1), we have,
$⟹$2(8 - 2y) - 3y = 2
$⟹$16 - 4y - 3y = 2
$⟹$7y = 14
$⟹$y = 2

Substitute the value of y in equation (1)
$⟹$2x - 3(2) = 2
$⟹$2x - 6 = 2
$⟹$2x = 8
$⟹$x = 4

$\therefore$ The values of x and y are 4 and 2 respectively.