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

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Answer 1 · 2014-11-13T04:53:03

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.