# How do you solve the system of equations: 5m + 2n = -8 ; 4m + 3n = 2?

Aug 21, 2015

$\left(m , n\right) = \left(- 4 , 6\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}} 5 m + 2 n = - 8$
[2]$\textcolor{w h i t e}{\text{XXXX}} 4 m + 3 n = 2$

Multiply [1] by 3, then [2] by 2, generating two equations with the same coefficient for $n$
[3}$\textcolor{w h i t e}{\text{XXXX}} 15 m + 6 n = - 24$
[4]$\textcolor{w h i t e}{\text{XXXX}} 8 m + 6 n = 4$

Subtract [4] from [3]
[5]$\textcolor{w h i t e}{\text{XXXX}} 7 m = - 28$

Divide both sides by 7
[6]$\textcolor{w h i t e}{\text{XXXX}} m = - 4$

Substitute $\left(- 4\right)$ for $m$ in [1]
[7]$\textcolor{w h i t e}{\text{XXXX}} 5 \left(- 4\right) + 2 n = - 8$

Simplify
[8]$\textcolor{w h i t e}{\text{XXXX}} 2 n = 12$

Divide by 2
[9]$\textcolor{w h i t e}{\text{XXXX}} n = 6$