Question

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

Answer 1

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.

`3x+2y= 12`
`-6x-4y=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.

`4x-8y=5`
`-3x+6y=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.