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

Jan 16, 2018

$x = - 5$
$y = 8$

#### 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:

$8 x = - 40$

Divide everything by $8$ and we have

$x = - 5$

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

$- \left(- 5\right) + 2 y = 21$

Now simplify and find $y$

$5 + 2 y = 21$

$2 y = 16$

Therefore,

$y = 8$

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

$\left(7\right) \left(- 5\right) + \left(2\right) \left(8\right) = - 19$

$- 35 + 16 = - 19$

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 $x$.