#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)#.
