algebra

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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 -

    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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