color(white)(aa)3x+3y=9aa3x+3y=9
color(red)(-4x+color(white)ay=3)−4x+ay=3
Multiiply the 2nd equation by -3−3. This will allow you to "cancel out" the yy terms by adding the equations together. This technique is usually called "linear combination" or sometimes "elimination".
-3(color(red)(-4x+y=3))−3(−4x+y=3)
color(red)(12x-3y=-9)12x−3y=−9
Rewrite with the first equation and add the two equations together.
color(white)(\a)3x+3y=color(white)(aa)9a3x+3y=aa9
color(red)(12x-3y=-9)12x−3y=−9
15x=015x=0
(15x)/15=0/15color(white)(aaa)15x15=015aaaDivide both sides by 15
x=0x=0
Substitute x=0x=0 into either of the original equations. I will pick the first equation.
3x+3y=93x+3y=9
3(0)+3y=93(0)+3y=9
3y=93y=9
(3y)/3=9/3color(white)(aaa)3y3=93aaaDivide both sides by 3
y=3y=3
The solution is (0,3)(0,3).
