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

1 Answer
Jan 16, 2018

Answer:

#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#.