# How do you solve 5x+y=5 and 10x + 3y = 20?

Apr 23, 2017

See explanation.

The system is:

## $\left\{\begin{matrix}5 x + y = 5 \\ 10 x + 3 y = 20\end{matrix}\right.$

If you multiply the first equation by $- 2$ the oefficients of $x$ will be opposite:

## $\left\{\begin{matrix}- 10 x - 2 y = - 10 \\ 10 x + 3 y = 20\end{matrix}\right.$

If you add both equations you get:

## $y = 10$

Now you can substitute the calcukated value to the first equation to calculate the value of $x$:

## $5 x + 10 = 5$

$5 x = - 5$

$x = - 1$