Posted by **lilmissluck** on Friday, January 7, 2011 at 5:41pm.

o How do you know when an equation has an infinite number of solutions?

o How do you know when an equation has no solution?

- algebra -
**Reiny**, Friday, January 7, 2011 at 6:59pm
If after you perform all proper steps and simplifications, the variables drop out and you end up with a TRUE statement, then there is an infinite number of solutions.

If after you perform all proper steps and simplifications, the variables drop out and you end up with a FALSE statement, then there is no solution.

e.g.

(x+1)^2 = x^2 + 2x + 1

x^2 + 2x + 1 = x^2 + 2x + 1

1=1 -----true, thus infinite numer of solutions

e.g.

3(2x + 5) = 6x+1

6x + 15 = 6x+1

15 = 1 ---- false, therefore no solution.

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