# How do you solve 3x - y = 10 and -x + y = -4?

Oct 4, 2016

$\left(3 , - 1\right)$

#### Explanation:

You have to eliminate either the $x$ or $y$ variable.

This system is easier to solve if you eliminate the $y$ variable then solve for x.

You can eliminate the $y$ variable by adding the 2 equations together.

$3 x - x$ becomes $2 x$

$- y + y$ becomes $0$ This is where $y$ is eliminated.

$10 - 4$ becomes $6$

You then left with ...

$2 x = 6$

Isolate x by dividing by $2$

$\frac{\cancel{2} x}{\cancel{2}} = \frac{6}{2}$

$x = \frac{6}{2}$

$x = 3$

Now substitute the value of $x$, 3, into either of the original equations.

I will substitute into the first equation.

$3 \left(3\right) - y = 10$

$9 - y = 10$

Subtract $9$ from both sides

$- y = 10 - 9$

$- y = 1$

Divide by $- 1$

$\frac{\cancel{- 1} y}{\cancel{- 1}} = \frac{1}{-} 1$

$y = \frac{1}{-} 1$

$y = - 1$

The answer is $\left(3 , - 1\right)$