Question 486241
Using your examples of x=12, y=5
:
One equation could be: x - 2y = 2
another equation: -x + 3y = 3
:
Add these two equations 
 x - 2y = 2
-x + 3y = 3
---------------addition eliminates x find y
y = 5
Find x using the 1st equation
x - 2(5) = 2
x - 10 = 2
x = 2 + 10
x = 12
:
Check solutions in the 2nd equation
-x + 3y = 3
-12 + 3(5) =
-12 + 15 = 3