# How do you solve the following system?: x +3y =-2 , -7x +y = -9

Mar 25, 2018

Here,$x + 3 y = - 2$
$\Rightarrow x = - 3 y - 2$ ----eqn 1
Substitute this value of x in $- 7 x + y = - 9$
We get $- 7 \left(- 3 y - 2\right) + y = - 9$
$\Rightarrow 21 y + 14 + y = - 9$
$\Rightarrow 22 y = - 9 - 14$
$\Rightarrow y = - \frac{23}{22}$ ----eqn 2
Now, substitute this value in $x + 3 y = - 2$
$\Rightarrow x + 3 \times - \frac{23}{22} = - 2$
$\Rightarrow x - \frac{69}{22} = - 2$
$\Rightarrow x = \frac{69}{22} - 2$
$\Rightarrow x = \frac{25}{22}$

So, $\left(x , y\right) = \left(\frac{25}{22} , - \frac{23}{22}\right)$

Hope this helps :)