# How do you solve the following system: 3x-y=12, 5x+2y=20 ?

Jun 3, 2018

$x = 4 , y = 0$

#### Explanation:

$3 x - y = 12$
$5 x + 2 y = 20$

We can start and find x by multiplying equation 1 by 2.

$2 \left(3 x - y = 12\right)$
$5 x + 2 y = 20$

$6 x - 2 y = 24$
$5 x + 2 y = 20$

Now we can add both equations together and cancel the y' s.

$6 x - 2 y = 24$
$11 x = 44$

Therefore, x = 4.

Now, we can back-substitute x to solve for y.

$6 \left(4\right) - 2 y = 24$
$24 - 2 y = 24$
$- 2 y = 0$
$y = 1$

Our solution set is (4, 1) or x = 4 and y = 1