How do you solve #2x+3y=6# and #y=2x-6# using substitution?

1 Answer
May 15, 2016

Answer:

#(x,y)=color(blue)(""(3,0))#
(see below for solution by substitution)

Explanation:

Given
[1]#color(white)("XXX")2x+3y=6#
[2]#color(white)("XXX")y=2x-6#

Since from [2] we have that #y=2x-6#
we can replace #y# with #(2x-6)# in [1]
to get
[3]#color(white)("XXX")2x+3(2x-6)=6#

Simplifying
[4]#color(white)("XXX")8x-18=6#

[5]#color(white)("XXX")rarr 8x=24#

[6]#color(white)("XXX")rarr x=3#

Since from [6] #x=3#
we can replace #x# with #(3)# in [2]
to get
[7]#color(white)("XXX")y=2(3)-6#

and simplifying
[8]#color(white)("XXX")y=0#