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24 November, 12:09

What is one of the solutions to the following system of equations?. y2 + x2 = 65. y + x = 7

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  1. 24 November, 12:21
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    X^2+y^2=65

    (x+y) = 7 = > y=7-x

    substitute in first equation

    x^2 + ((7-x) ^2=65

    expand and simplify

    x^2+x^2-14x+49=65

    2x^2-14x-16=0

    2 (x^2-7x-8) = 0

    Factorize

    2 (x-8) (x+1) = 0

    x=8, or x=-1

    take x=8, solve for y=+/-1

    Take y=+/-1, x=+/-8

    So the solutions are

    {8,1},{-8,-1},{8,-1},{-8,1

    Out of these, only {8,-1} satisfies x+y=7, so this is the only solution.
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