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

1 Answer
Oct 26, 2015

Answer:

Re-write one of the equations into the form
#color(white)("XXX")x= "an expression"#
then substitute the "expression" for #x# in the other equation.
#color(white)("XXX")(x,y)=(-9,-4)#

Explanation:

Given
[1]#color(white)("XXX")-2x+5y=-2#
[2]#color(white)("XXX")x-3y=3#

Rearranging the terms of [2]
[3]#color(white)("XXX")x=3y+3#

Substituting #3y+3# for #x# in [1]
[4]#color(white)("XXX")-2(3y+3)+5y = -2#

Simplifying
[5]#color(white)("XXX")-6y-6+5y=-2#

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

Substituting #(-4)# for #y# in [2]
[7]#color(white)("XXX")x-3(-4)=3#

[8]#color(white)("XXX")x=-9#