How do you solve the following system?: # -2x+3y=5, -x+y=-3 #

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Answer 1 · 2017-06-28T00:49:48

#x=14, y-11#

#color(white)(+)-2x+3y=5#
#color(white)(+)#
#color(white)(+)-x+y=-3#

Let's use substitution! We need to solve for #y# in the second equation:
#-x+y=-3#

#y=-3+x#

Let's substitute #(-3+x)# for #y# in the first equation

#-2x+3y=5#

#-2x+3(-3+x)=5#

#-2x-9+3x=5#

#x=14#

Now we have #x#, let's solve for #y#:

#-2(14)+3y=5#

#-28+3y=5#

#3y=33#

#y=11#

Now we have our solutions, but to double-check, let's solve the second equation, using #14# and #11# for #x# and #y#:

#-x+y=-3#

#-(14)+11# should give us #-3#, if we did everything correctly

#-3=-3#, so we were right!