How do you solve the following system?: #5x-7y=22 , 3x+3y=-21 #

1 Answer
MathFact-orials.blogspot.com
May 15, 2018

#(x,y)=(-9/4,-19/4)#

Explanation:

We have

#5x-7y=22#
#3x+3y=-21#

Let's notice that we can divide the second equation by 3:

#x+y=-7#

I'll solve for #x#:

#x=-7-y#

And now substitute into the first equation:

#5(-7-y)-7y=22#

#-35-5y-7y=22#

#-12y=57#

#y=-57/12=-19/4#

#:. 3x+3(-19/4)=-21#

#3x-57/4=-21#

#12x-57=-84#

#12x=-27=>x=-27/12=-9/4#

Graphed, it looks like this:

graph{(5x-7y-22)(3x+3y+21)=0[-10,10,-10,0]}

(On my screen, the graphing utility is sometimes cutting off one part of one of lines. To fix, hover over the graph and zoom in/out and that seems to fix it).

Related questions
See all questions in Systems Using Substitution
Impact of this question
2065 views around the world
You can reuse this answer
Creative Commons License