Asked by lilmissluck
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?
o How do you know when an equation has no solution?
Answers
Answered by
Reiny
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.
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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