algebra

write a pair of equations that have exactly two solutions. (at least one equation is not linear) any links to help?

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  1. For the nonlinear equation, it can be something like:
    (x + 2) * (x - 5)

    and then FOIL it out like this:

    x^2 - 3x - 10

    You can substitute any two different integers for 2 and -5 there, and it will be a nonlinear function with two solutions.

    For a linear equation, it could be as simple as the square root of x. Let's say we have the square root of 4. This has two solutions, since 2^2 = 4, and -2^2 = 4.

    I'd send you a link, but I can't in this forum -- but Khan Academy Algebra has great resources on this.

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  2. a straight line can intersect a parabola in two places
    ... the intersection points are the simultaneous solutions

    linear form ... y = m x + b ... m and/or b could be zero

    quadratic form ... y = a x^2 + b x + c ... b and/or c could be zero

    fill in some values and check with a graphing program

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  3. to tyger ... the √ function is not linear

    but it makes no difference in this case

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