# Question 6a010

Nov 22, 2016

Consider the following system.

$\left\{\begin{matrix}x + y = 5 \\ - 2 x + 5 y = 4\end{matrix}\right.$

Now, the addition/subtraction method is used to eliminate one of the variables. We can do this to the above equation for $x$ by multiplying the first equation by $2$ and using the addition method.

1)" "2(x + y) = 2(5)#

$2 x + 2 y = 10$

The system becomes:

$\left\{\begin{matrix}2 x + 2 y = 10 \\ - 2 x + 5 y = 4\end{matrix}\right.$, which can be solved by elimination:

$0 x + 7 y = 14$

$y = 2$

$x + y = 5$

$x + 2 = 5$

$x = 3$

Practice exercises:

1. Solve each system through elimination.

a) $\left\{\begin{matrix}x - 6 y = - 1 \\ 4 x + y = 21\end{matrix}\right.$

b) $\left\{\begin{matrix}3 x + 4 y = - 2 \\ 7 x - 3 y = 20\end{matrix}\right.$

Hopefully this helps, and good luck!