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

1 Answer

Answer:

#(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).