# How do you solve the following system of equations?: 4x – y = 14 , -3x + 3y=10?

Dec 19, 2015

$\left(x , y\right) = \left(\frac{52}{9} , \frac{82}{9}\right)$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXX}}$(not all answers are pretty)

#### Explanation:

Solving by Substitution
Given
[1]$\textcolor{w h i t e}{\text{XXX}} 4 x - y = 14$
[2]$\textcolor{w h i t e}{\text{XXX}} - 3 x + 3 y = 10$

Re-write [1] as
[3]$\textcolor{w h i t e}{\text{XXX}} y = 4 x - 14$

Substitute $4 x - 14$ (from [3]) for $y$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} - 3 x + 3 \left(4 x - 14\right) = 10$

Simplify
[5]$\textcolor{w h i t e}{\text{XXX}} 9 x - 42 = 10$

[6]$\textcolor{w h i t e}{\text{XXX}} 9 x = 52$

[7]$\textcolor{w h i t e}{\text{XXX}} x = \frac{52}{9}$

Substituting $\left(\frac{52}{9}\right)$ for $x$ in [1]
[8]$\textcolor{w h i t e}{\text{XXX}} 4 \times \left(\frac{52}{9}\right) - y = 14$

[9]$\textcolor{w h i t e}{\text{XXX}} y = \frac{208}{9} - 14 = \frac{208 - 126}{9} = \frac{82}{9}$