How do you solve the following system using substitution?: #x-3y=2, x+y=-10#

1 Answer
Oct 21, 2015

Answer:

#(x,y) = (-7,-3)#

Explanation:

Given
[1]#color(white)("XXX")x-3y=2#
[2]#color(white)("XXX")x+y=-10#

Rearrange [1], isolating #x# on one side:
[3]#color(white)("XXX")x=3y+2#

Substitute #(3y+2)# for #x# in [2]
[4]#color(white)("XXX")(3y+2)+y=-10#

Simplify
[5]#color(white)("XXX")4y=-12#

[6]#color(white)("XXX")y=-3#

Substitute #(-3)# for #y# in [1]
[7]#color(white)("XXX")x-3(-3) = 2#

[8]#color(white)("XXX")x+9 = 2#

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