# How do you solve the system of equations 4x - 4y = 10 and  3x + 2y = 5?

$x = 2$
$y = - 0.5$

#### Explanation:

$4 x - 4 y = 10$
$3 x + 2 y = 5$
$x - y = 2.5$
$x = y + 2.5$
$3 \left(y + 2.5\right) + 2 y = 5$
$3 y + 7.5 + 2 y = 5$
$5 y = 5 - 7.5$
$5 y = - 2.5$
$y = - 0.5$
$x = - 0.5 + 2.5$
$x = 2$
Check
$4 x - 4 y = 4 \times 2 - 4 \times \left(- 0.5\right) = 8 + 2 = 10$
$3 x + 2 y = 3 \times 2 + 2 \times \left(- 0.5\right) = 6 - 1 = 5$

Verified