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

Mar 28, 2018

$x = - 1$
$y = - 2$

#### Explanation:

Solve by substitution:
$x + y = - 3$
$y = 2 x$

Since you were already given that $y = 2 x$ plug it into the first equation to solve for x:

$x + \left(2 x\right) = - 3$ (Combine like terms)
$3 x = - 3$ (Divide by 3 to isolate variable)
$x = - 1$

Now that you have solved for x, plug it into either equation to solve for y:

$y = 2 \left(- 1\right)$
$y = - 2$

Check the answer by plugging in both variables into equation 1:

$- 1 + \left(- 2\right) = - 3$
$- 3 = - 3$