How do you solve the following system?:  x=-3y -6, -x-8y=32

Dec 3, 2015

This set of equation has one solution:

$\left\{\begin{matrix}x = - 20 \frac{2}{5} \\ y = - 4 \frac{4}{5}\end{matrix}\right.$

Explanation:

$\left\{\begin{matrix}x = - 3 y - 6 \\ - x - 8 y = 32\end{matrix}\right.$

First I ordered both equations by placing the variables on the left side and free terms on the right side.

$\left\{\begin{matrix}x + 3 y = - 6 \\ - x - 8 y = 32\end{matrix}\right.$

We can see that variable $x$ has opposite coefficients so if I add both equations I get equation with one unknown:

$- 5 y = 24$

$y = - \frac{24}{5} = - 4 \frac{4}{5}$

Now I substitute calculated $x$ to the first equation:

$x = - 3 \cdot \left(- \frac{24}{5}\right) - 6$

$x = - \frac{72}{5} - 6$

$x = - \frac{72}{5} - \frac{30}{5}$

$x = - \frac{102}{5} = - 20 \frac{2}{5}$