How do you solve the system using the elimination method for 3x-4y=18 and x+3y=-7?

1 Answer
Mar 22, 2018

Answer:

#(x,y)=(2,-3)#
See below for solution by elimination

Explanation:

Given
[1]#color(white)("XXX")3x-4y=18#
[2]#color(white)("XXX")x+3y=-7#

If we multiply [2] by #3# we can generate an equation with the same #x# coefficient as that in [1]
[3]#color(white)("XXX")3x+9y=-21#

We can now eliminate the #x# term by subtracting [1] from [3]
[4]#color(white)("XXX")13y=-39#

After dividing both sides of [4] by #13#
[5]#color(white)("XXX")y=-3#

Substituting #(-3)# for #y# in [2}
[6]#color(white)("XXX")x+3 * (-3)=-7#

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

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