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

Re-arrange [1] and [2] into standard form to get (respectively)
[3]$\textcolor{w h i t e}{\text{XXX}} x - 2 y = 4$
[4]$\textcolor{w h i t e}{\text{XXX}} 4 x - 4 y = - 17$

Since this was asked under "Systems Using Substitution"
Re-write [3] as $x$ in terms of $y$
[5]$\textcolor{w h i t e}{\text{XXX}} x = 2 y + 4$

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

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

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

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

Substituting $\left(- \frac{33}{4}\right)$for $y$ in [3]
[10]$\textcolor{w h i t e}{\text{XXX}} x - 2 \left(- \frac{33}{4}\right) = 4$

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

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

[These values may look a bit ugly, but substituting back into equations [1] and [2] verify that they are correct.]