How do you solve the system of equations algebraically #7x+y=9, 5x-y=15#?

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Answer 1 · 2016-12-16T03:04:15

#(x,y)=(2,-5)#

We can add the two equations together to eliminate the #y# term, solve for #x#, then substitute in. Like this:

#7x+y=9#
#5x-y=15#

#12xcolor(white)(000)=24#

#x=2#

Substituting into either of the original equations will give us #y# (I'll do both to show it doesn't matter):

#7x+y=9#

#7(2)+y=9#

#14+y=9#

#y=-5#

~~~~~

#5x-y=15#

#5(2)-y=15#

#10-y=15#

#-y=5#

#y=-5#