# How do you determine the solution in terms of a system of linear equations for x + 3y = -3, x - 4y = 11?

Oct 10, 2015

$\left(x , y\right) = \left(3 , - 2\right)$

#### Explanation:

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

Subtract [2] from [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 7 y = - 14$

Divide both sides of [3] by $7$
[4]$\textcolor{w h i t e}{\text{XXX}} y = - 2$

Substitute $\left(- 2\right)$ for $y$ in [1]
[5]$\textcolor{w h i t e}{\text{XXX}} x + 3 \left(- 2\right) = - 3$

[6]$\textcolor{w h i t e}{\text{XXX}} x - 6 = - 3$

[7]$\textcolor{w h i t e}{\text{XXX}} x = 3$

Recommendation: verify by plugging $\left(3 , - 2\right)$ for (x,y) back into the original equations.