2x + 4y = 20
you can solve for x in terms of y:
2x + 4y = 20
2x = 20 - 4y
x = (20 - 4y) / 2
x = 10 - 2y
and then plug in your new x value back into the OTHER equation and solve for y:
12x + 3y = 36
12(10 - 2y) + 3y = 36
120 - 24y + 3y = 36
120 - 21y = 36
-21y = 36 - 120
-21y = -84
21y = 84
y = 4
Then take y and plug it back in for x:
x = 10 - 2y
x = 10 - 2(4)
x = 10 - 8
x = 2
So your final answers are:
x = 2
y = 4
You could also use this method three other ways:
1. Using the second equation (as above) but finding y in terms of x:
2x + 4y = 20
4y = 20 - 2x
y = (20 - 2x) / 4
y = 5 - (x/2)
12x + 3y = 36
12x + 3*(5 - (x/2)) = 36
12x + 15 - (3/2)x = 36
(21/2)x + 15 = 36
10.5x = 21
x = 2
y = 5 - (2/2)
y = 4
2. Using the first equation and finding x in terms of y:
12x + 3y = 36
12x = 36 - 3y
x = (36 - 3y) / 12
x = 3 - (y/4)
2x + 4y = 20
2*(3 - (y/4)) + 4y = 20
6 - (1/2)y + 4y = 20
6 + 3.5y = 20
3.5y = 14
y = 4
x = 3 - (4/4)
x = 2
3. Using the first equation and finding y in terms of x:
12x + 3y = 36
3y = 36 - 12x
y = (36 - 12x) / 3
y = 12 - 4x
2x + 4y = 20
2x + 4*(12 - 4x) = 20
2x + 48 - 16x = 20
48 - 14x = 20
-14x = -28
14x = 28
x = 2
y = 12 - 4(2)
y = 12 - 8
y = 4
Use whichever method you find easiest - you'll get the same answers either way.