# How do you solve the system -3(5+x)=y and 5(x-3)=2y+4?

Jul 7, 2015

$\left(x , y\right) = \left(- 1 , - 12\right)$

#### Explanation:

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

Replace $y$ in [2] with $- 3 \left(5 + x\right)$ as specified in [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$5 \left(x - 3\right) = 2 \left(- 3 \left(5 + x\right)\right) + 4$

Simplifying
[4]$\textcolor{w h i t e}{\text{XXXX}}$$5 x - 15 = - 30 - 6 x + 4$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$11 x = - 11$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 1$

Substituting $x = - 1$ back in [1]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$- 3 \left(5 - 1\right) = y$
[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 12$