How do you solve #3x+3y=9, -4x+y=3#?

1 Answer
Nov 18, 2016

Answer:

Use linear combination to get the solution #(0,3)#.

Explanation:

#color(white)(aa)3x+3y=9#
#color(red)(-4x+color(white)ay=3)#

Multiiply the 2nd equation by #-3#. This will allow you to "cancel out" the #y# terms by adding the equations together. This technique is usually called "linear combination" or sometimes "elimination".

#-3(color(red)(-4x+y=3))#

#color(red)(12x-3y=-9)#

Rewrite with the first equation and add the two equations together.

#color(white)(\a)3x+3y=color(white)(aa)9#
#color(red)(12x-3y=-9)#

#15x=0#

#(15x)/15=0/15color(white)(aaa)#Divide both sides by 15

#x=0#

Substitute #x=0# into either of the original equations. I will pick the first equation.

#3x+3y=9#

#3(0)+3y=9#

#3y=9#

#(3y)/3=9/3color(white)(aaa)#Divide both sides by 3

#y=3#

The solution is #(0,3)#.