# How do you solve –4x + 7y = –10 and x – 5y = 9?

Mar 14, 2018

x=-1, y=-2

#### Explanation:

Solve for x in one equation, and then substitute x for your solution in the second equation to solve for y, then back-solve for x.

We'll start by solving for x in the second equation, since that is easiest:

x-5y=9 rArr color(blue)(x=9+5y

Now that we know x with respect to y, we can use that in the first equation:

$- 4 \textcolor{b l u e}{x} + 7 y = - 10$

$- 4 \textcolor{b l u e}{\left(9 + 5 y\right)} + 7 y = - 10 \Rightarrow - 36 - 20 y + 7 y = - 10$

$- 13 y = 26 \Rightarrow \textcolor{red}{y = - 2}$

Now we know the value of y for this system of equations. Plugging that back into our relation with x:

$x = 9 + 5 \left(\textcolor{red}{- 2}\right) \Rightarrow x = 9 - 10 \Rightarrow \textcolor{g r e e n}{x = - 1}$