# How do you solve the system using elimination x=-4y  and 3x+5y=-11?

Jun 4, 2015

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

Using [1] substitute $\left(- 4 y\right)$ for all occurrences of $x$ in [2]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$3 \left(- 4 y\right) + 5 y = - 11$
Simplifying
[4]$\textcolor{w h i t e}{\text{XXXX}}$$- 7 y = - 11$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$y = \frac{11}{7}$

Substituting $\frac{11}{7}$ for $y$ back into [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 4 \left(\frac{11}{7}\right) = 1 \frac{44}{7}$

$\left(x , y\right) = \left(- \frac{44}{7} , \frac{11}{7}\right)$