# How do you know if a solution is "no solution" or "infinite" when using the substitution method?

Nov 13, 2014

For an answer to have an infinite solution, the two equations when you solve will equal $0 = 0$.

Here is a problem that has an infinite number of solutions.

$3 x + 2 y = 12$
$- 6 x - 4 y = 24$

If you solve this your answer would be $0 = 0$ this means the problem has an infinite number of solutions.

For an answer to have no solution both answers would not equal each other.

Here is a problem that has no solution.

$4 x - 8 y = 5$
$- 3 x + 6 y = 11$

Again, if you solve this your answer would be $0 = 59$, this is obviously not true, 0 does not equal 59 so this problem would have no solution.