x - y = 11
2x + y = 19
add the top equation to the bottom
x - y = 11
3x + 0y = 30
divide the bottom equation by 3 on both sides
x - y = 11
x + 0y = 10
Now we know x = 10
multiply the bottom equation by -1 on both sides
x - y = 11
-x + 0y = -10
add the bottom equation to the top
0x - y = 1
-x + 0y = -10
multiply the top equation by -1 on both sides
0x + y = -1
-x + 0y = -10
Now we know y = -1
Answer: x = 10, y = -1