In a system of equations using the elimination method...?

Question

what happens if both variables cancell out?

and if everything cancells out (variables and regular numbers)

Answer 1

You have either "no solution" (which means the lines are parallel) or "infinitely many solutions" (which means two expressions for the same line).

If after the variables cancel you get something stupid (like 2 = 3 or perhaps -9 = 14), you've got a "no solution" problem. No matter what values you pick for x and y, there's no way you can get the system of equations to work out.

If you have a true statement like 4 = 4, there are infinitely many solutions. For every possible value of x there is an equivalent value of y that will work in the system.

Answer 2

Use a different method.