18 - 2(3x-y) = 0
18 - 6x + 2y = 0
-6x + 2y = -18
.
4x -(x-3y) = 9
4x - x + 3y = 9
3x + 3y = 9
.
-6x + 2y = -18
3x + 3y = 9
multiply the bottom equation byt 2 on both sides
-6x + 2y = -18
6x + 6y = 18
add the top equation to the bottom
-6x + 2y = -18
0x + 8y = 0
divide the bottom equation by 8 on both sides
-6x + 2y = -18
0x + y = 0
Now we know y = 0
multiply the bottom equation by -2 on both sides
-6x + 2y = -18
0x - 2y = 0
add the bottom equation to the top
-6x + 0y = -18
0x - 2y = 0
divide the top equation by -6 on both sides
x + 0y = 3
0x - 2y = 0
Now we know x = 3
Answer: x = 3, y = 0