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how do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

  • math116 -

    The question of how many solutions,
    if any,usually comes up when solving
    2 equations simutaneously. First, we
    need to define solution: The solution is the point where the two lines inter-
    sect. I F they do not INTERSECT, there
    is no solution. Parallel lines do not
    INTERSECT and have no solution. We
    identify parallel lines by the fact that they have = slopes. But their
    Y-intercepts are different.

    Now surpose 2 equations have = slopes AND = Y-intercepts, Then, they repre-
    sent the same line and all points on
    the line intersect.Therefore, we have an INFINITE number of solutions.

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