# How do you find the solution set for x-y=11, 3x+10y=-6?

Aug 6, 2015

$\left(x , y\right) = \left(8 , - 3\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$x - y = 11$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$3 x + 10 y = - 6$

Multiply [1] by 3
[3]$\textcolor{w h i t e}{\text{XXXX}}$$3 x - 3 y = 33$

Subtract [3] from [2]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$13 y = - 39$

Divide [4] by 13
[5]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 3$

Substitute $\left(- 3\right)$ for $y$ in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$x- (-3) = 11#

Simplify
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 = 11$

Subtract 3 from both sides of [7]
[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = 8$