Question

How do you solve the system of equations `7x + 2y = - 19` and `- x + 2y = 21`?

Answer 1

`x=-5`
`y=8`

Explanation:

So, already we don’t have to change the equations in any way, seen as the `y`’s are the same. The simplest way to do this is by the elimination method.

First, we’re going to eliminate the `y`’s. As both are positive, we’re going to minus them. As we’re subtracting the `y`’s, we have the do it with the `x`’s and the answers.

We’re left with:

`8x=-40`

Divide everything by `8` and we have

`x=-5`

Substitute `x=-5` into either equation to get `y`. I’ll go with the simplest.

`-(-5)+2y=21`

Now simplify and find `y`

`5+2y=21`

`2y=16`

Therefore,

`y=8`

If you want to check, then substitute `x` and `y` into the other equation.

`(7)(-5)+(2)(8)=-19`

`-35+16=-19`

which is a correct statement.

Side note: I’ve used brackets instead of multiplication symbols as it makes it easier (at least for me) to see what’s been multiplied and what is `x`.