Three times one number added to another number is 18. Twice the first number minus the other number is 12. Find the numbers

3x + y = 18

2x - y = 12

we must make both equations have only one variable

we first add the equations top to bottom, and get

5x = 30

we then divide by 5, and get x = 6

now we sub 6 in for x, and solve for y

3x + y = 18 y = 18 - 3x

y = 18 - 18

y = 0

the first number is 6, the second number is 0