# How do you use the addition and subtraction method to solve a linear system?

Nov 1, 2014

Let us solve the linear system below.

$\left\{\begin{matrix}3 x + y = 7 \\ x + 2 y = - 1\end{matrix}\right.$

The goal is to eliminate one of the variables by addition or subtraction so that the value of the other variable can be found.

By multiply the first equation by 2,

$\implies \left\{\begin{matrix}6 x + 2 y = 14 \\ x + 2 y = - 1\end{matrix}\right.$

by subtracting the second equation from the first equation,

$\implies 5 x = 15 \implies x = 3$

By plugging $x = 3$ in the first equation of the original system,

$\implies 3 \left(3\right) + y = 7 \implies 9 + y = 7 \implies y = - 2$

Hence, the solution is $\left(x , y\right) = \left(3 , - 2\right)$.

I hope that this was helpful.