# How do you solve the following system?:  x+3y=6, -x+y=-3

Feb 1, 2016

I found:
$x = \frac{15}{4}$
$y = \frac{3}{4}$

#### Explanation:

I would try to add in columns the two equations:
$\left\{\begin{matrix}x + 3 y = 6 \\ - x + y = - 3\end{matrix}\right.$
color(red)(0+4y=3
so that $y = \frac{3}{4}$
substitute this value into the first equation:
$x + \left(3 \cdot \textcolor{b l u e}{\frac{3}{4}}\right) = 6$
$4 x + 9 = 24$
$x = \frac{15}{4}$