# How do you solve this system of equation: 6x + z = - 7 and - 4x + 2z = - 6?

Apr 4, 2018

$\left(x , z\right) = \left(- \frac{1}{2} , - 4\right)$

#### Explanation:

$z = - 7 - 6 x$ solve for $z$ in terms of $x$ in the first equation
$- 4 x + 2 \left(- 7 - 6 x\right) = - 6$ plug into the other equation
$- 4 x - 14 - 12 x = - 6$ distribute
$- 14 - 16 x = - 6$ combine
$- 16 x = 8$
$x = - \frac{1}{2}$

Now, going back to the other equation
$6 \left(- \frac{1}{2}\right) + z = - 7$
$- 3 + z = - 7$
$z = - 4$