# How do you solve 5x + 4y = 6 and -2x - 3y = -1?

Aug 10, 2015

$\left(x , y\right) = \left(2 , - 1\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$5 x + 4 y = 6$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$- 2 x - 3 y = - 1$

Multiply [1] by 2 and [2] by $\left(- 5\right)$ to get 2 equations with identical coefficients for $x$
[3]$\textcolor{w h i t e}{\text{XXXX}}$$10 x + 8 y = 12$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$10 x + 15 y = 5$

Subtract [4] from [3]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$- 7 y = 7$

Divide both sides by $\left(- 7\right)$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 1$

Substitute $\left(- 1\right)$ for $y$ in [1]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$5 x + 4 \left(- 1\right) = 6$

Simplify
[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = 2$