How do you solve #8x+5y=-4# and # -5x+y=19# using substitution?

1 Answer
Alan P.
May 26, 2016

#(x,y)=color(blue)(""(-3,4))#
(see below for solution using substitution).

Explanation:

Given
[1]#color(white)("XXX")8x+5y=-4#
[2]#color(white)("XXX")-5x+y=19#

Note that [2] can be re-written as
[3]#color(white)("XXX")y=5x+19#

We can therefore substitute #(5x+19)# in place of #y# in [1]
[4]#color(white)("XXX")8x+5(5x+19)=-4#

[5]#color(white)("XXX")33x+95=-4#

[6]#color(white)("XXX")33x=-99#

[7]#color(white)("XXX")x=-3#

We can now substitute #(-3)# in place of #x# in [3]
[8]#color(white)("XXX")y=5(-3)+19#

[9]#color(white)("XXX")y=4#

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