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

1 Answer
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.

#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.