# How do you solve 3x+3y=9, -4x+y=3?

Nov 18, 2016

Use linear combination to get the solution $\left(0 , 3\right)$.

#### Explanation:

$\textcolor{w h i t e}{a a} 3 x + 3 y = 9$
$\textcolor{red}{- 4 x + \textcolor{w h i t e}{a} y = 3}$

Multiiply the 2nd equation by $- 3$. This will allow you to "cancel out" the $y$ terms by adding the equations together. This technique is usually called "linear combination" or sometimes "elimination".

$- 3 \left(\textcolor{red}{- 4 x + y = 3}\right)$

$\textcolor{red}{12 x - 3 y = - 9}$

Rewrite with the first equation and add the two equations together.

$\textcolor{w h i t e}{\setminus a} 3 x + 3 y = \textcolor{w h i t e}{a a} 9$
$\textcolor{red}{12 x - 3 y = - 9}$

$15 x = 0$

$\frac{15 x}{15} = \frac{0}{15} \textcolor{w h i t e}{a a a}$Divide both sides by 15

$x = 0$

Substitute $x = 0$ into either of the original equations. I will pick the first equation.

$3 x + 3 y = 9$

$3 \left(0\right) + 3 y = 9$

$3 y = 9$

$\frac{3 y}{3} = \frac{9}{3} \textcolor{w h i t e}{a a a}$Divide both sides by 3

$y = 3$

The solution is $\left(0 , 3\right)$.