How do you solve the following system?:  x + 3-2y=7 , x=-3x + 4y-17

Mar 15, 2018

$\left(x , y\right) = \left(- \frac{25}{2} , - \frac{33}{4}\right)$

Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} x + 3 - 2 y = 7$
$\textcolor{w h i t e}{\text{XXX}} x = - 3 x + 4 y - 17$

Re-arrange  and  into standard form to get (respectively)
$\textcolor{w h i t e}{\text{XXX}} x - 2 y = 4$
$\textcolor{w h i t e}{\text{XXX}} 4 x - 4 y = - 17$

Since this was asked under "Systems Using Substitution"
Re-write  as $x$ in terms of $y$
$\textcolor{w h i t e}{\text{XXX}} x = 2 y + 4$

Then substitute $\left(2 y + 4\right)$ for $x$ in 
$\textcolor{w h i t e}{\text{XXX}} 4 \left(2 y + 4\right) - 4 y = - 17$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} 8 y + 16 - 4 y = - 17$

$\textcolor{w h i t e}{\text{XXX}} 4 y = - 33$

$\textcolor{w h i t e}{\text{XXX}} y = - \frac{33}{4}$

Substituting $\left(- \frac{33}{4}\right)$for $y$ in 
$\textcolor{w h i t e}{\text{XXX}} x - 2 \left(- \frac{33}{4}\right) = 4$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} x + \frac{33}{2} = \frac{8}{2}$

$\textcolor{w h i t e}{\text{XXX}} x = - \frac{25}{2}$

[These values may look a bit ugly, but substituting back into equations  and  verify that they are correct.]