How to solve a system of equations? Help please

First you have to equalize either the x or the y. I would choose the x.

so multiply the second equation by -6 to make the X= -12 (to equalize it with the top x)

12x+3y=36
-12x+4y=-120

7y=-84

divide by 7

X= -12

then plug in -12 into either of the original equations

12x + 3y = 36 divide both sides by 3
4x + y = 12 subtract 4x from both sides
y = 12 - 4x

2x + 4y = 20 substitute (12 - 4x) for y
2x + 4(12 - 4x) = 20 distribute the 4 on the left
2x + 48 - 16x = 20 combine like terms
48 - 14x = 20 add 14x to both sides
48 = 20 + 14x subtract 20 from both sides
28 = 14x divide both sides by 14
x = 2 ANSWER

12x + 3y = 36 substitute 2 in for x
12(2) + 3y = 36 simplify
24 + 3y = 36 subtract 24 from both sides
3y = 12 divide both sides by 3
y = 4 ANSWER

check work
12(2) + 3(4) = 36
24 + 12 = 36
36 = 36

2(2) + 4(4) = 20
4 + 16 = 20
20 = 20

x=2, y=4
12(2)+3(4)=36
24+12=36
36=36
2(2)+4(4)=20
2^2+4^2=20
4+16=20
20=20

12x-36=-3y
-4x+12=y

2x-20=-4y
-.5x+5=y

-4x+12 = -.5x+5
-3.5x = -7
x = 2

y = -4(2)+12
y = 4