How do you solve the system of equations 7x + 2y = - 197x+2y=−19 and - x + 2y = 21−x+2y=21?

1 Answer
KatieW · Stefan V.
Jan 16, 2018

x=-5x=−5
y=8y=8

Explanation:

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

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

We’re left with:

8x=-408x=−40

Divide everything by 88 and we have

x=-5x=−5

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

-(-5)+2y=21−(−5)+2y=21

Now simplify and find yy

5+2y=215+2y=21

2y=162y=16

Therefore,

y=8y=8

If you want to check, then substitute xx and yy into the other equation.

(7)(-5)+(2)(8)=-19(7)(−5)+(2)(8)=−19

-35+16=-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 xx.

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