# How do you solve 4x - y = 6 and 3x + y = 1?

Feb 11, 2016

$x = 1 , y = - 2$

#### Explanation:

Notice that when the two equations are added to one another, the $y$ and $- y$ terms will cancel. This is opportune because we will be left with just $x$ terms.

{:(color(white)("(")4x,-y,=6," "),("("3x,+y,=1")",+),(color(white)("(")color(blue)(7x),cancel(+0y),color(blue)(=7)," "):}

The resulting equation $7 x = 7$ can be divided by $7$ on both sides:

(7x)/7=7/7" "" "=>" "" "color(red)(x=1

This can be substituted into either equation to solve for $y$. I'll choose the second equation.

$3 \textcolor{red}{x} + y = 1 \text{ "" "=>" "" } 3 \textcolor{red}{\left(1\right)} + y = 1$

Solve the resulting equation:

$3 + y = 1$

color(green)(y=-2