Question

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

Answer 1

`(3,-1)`

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.

`3x-x` becomes `2x`

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

`10-4` becomes `6`

You then left with ...

`2x=6`

Isolate x by dividing by `2`

`(cancel2x)/cancel2=6/2`

`x=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(3)-y=10`

`9-y=10`

Subtract `9` from both sides

`-y=10-9`

`-y=1`

Divide by `-1`

`(cancel(-1)y)/(cancel(-1))=1/-1`

`y=1/-1`

`y=-1`

The answer is `(3,-1)`