# How do you solve the system using the elimination method for 4x-y=9 and x-3y=16?

Jul 7, 2015

$\left(x , y\right) = \left(1 , - 5\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$4 x - y = 9$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x - 3 y = 16$

Multiply [2] by 4 to obtain the same coefficient of $x$ as in [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$4 x - 12 y = 64$

Subtract [1] from [3]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$- 11 y = 55$

Solve for $y$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 5$

Substitute $y = - 5$ back into [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$4 x - \left(- 5\right) = 9$

Solve for $x$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$4 x = 4$

[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = 1$