# How do you solve -4x+y=-11 and 2x-3y=5?

Nov 30, 2015

$\left(x , y\right) = \left(\frac{14}{5} , \frac{1}{5}\right)$

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} - 4 x + y = - 11$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y = 5$

Multiply [2] by $2$ giving $x$ a coefficient of the same magnitude as in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x - 6 y = 10$

Add [1] and [3], eliminating the $x$ term
[4]$\textcolor{w h i t e}{\text{XXX}} - 5 y = - 1$

Divide both sides of [4] by $\left(- 5\right)$
[6]$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{5}$

Multiply [1] by $3$ giving $y$ a coefficient of the same magnitude as in [2]
[7]$\textcolor{w h i t e}{\text{XXX}} - 12 x + 3 y = - 33$

Add [2] and [7], eliminating the $y$ term
[8]$\textcolor{w h i t e}{\text{XXX}} - 10 x = - 28$

Divide both sides of [8] by $\left(- 10\right)$
[9]$\textcolor{w h i t e}{\text{XXX}} x = \frac{14}{5}$