# How do you solve the following system?: 5x-7y=22 , 3x+3y=-21

$\left(x , y\right) = \left(- \frac{9}{4} , - \frac{19}{4}\right)$

#### Explanation:

We have

$5 x - 7 y = 22$
$3 x + 3 y = - 21$

Let's notice that we can divide the second equation by 3:

$x + y = - 7$

I'll solve for $x$:

$x = - 7 - y$

And now substitute into the first equation:

$5 \left(- 7 - y\right) - 7 y = 22$

$- 35 - 5 y - 7 y = 22$

$- 12 y = 57$

$y = - \frac{57}{12} = - \frac{19}{4}$

$\therefore 3 x + 3 \left(- \frac{19}{4}\right) = - 21$

$3 x - \frac{57}{4} = - 21$

$12 x - 57 = - 84$

$12 x = - 27 \implies x = - \frac{27}{12} = - \frac{9}{4}$

Graphed, it looks like this:

graph{(5x-7y-22)(3x+3y+21)=0[-10,10,-10,0]}

(On my screen, the graphing utility is sometimes cutting off one part of one of lines. To fix, hover over the graph and zoom in/out and that seems to fix it).