# How do you solve 3x+6y=-6 and -7x+y=29 using substitution?

Apr 1, 2018

$\left(x , y\right) = \left(- 4 , 1\right)$

#### Explanation:

Solve one of these equations for $y$ to make substitution possible. The second equation appears best suited for this:

$- 7 x + y = 29$

$y = 7 x + 29$

We can now replace all instances of $y$ in the first equation with $7 x + 29 :$

$3 x + 6 \left(7 x + 29\right) = - 6$

$3 x + 42 x + 174 = - 6$

$45 x = - 6 - 174$

$45 x = - 180$

$x = - \frac{180}{45}$

$x = - 4$

To find $y ,$ plug in the result above into either of the two equations. We solved the second one for $y ,$ so that will be the easiest one to use:

$y = 7 \left(- 4\right) + 29$

$y = 1$