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27 March, 23:50

What is the solution set of x2 + y2 = 26 and x - y = 6? A. { (5, - 1), (-5, 1) } B. { (1, 5), (5, 1) } C. { (-1, 5), (1, - 5) } D. { (5, - 1), (1, - 5) }.

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  1. 27 March, 23:55
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    He two equations given are

    x^2 + y^2 = 26

    And

    x - y = 6

    x = y + 6

    Putting the value of x from the second equation to the first equation, we get

    x^2 + y^2 = 26

    (y + 6) ^2 + y^2 = 26

    y^2 + 12y + 36 + y^2 = 26

    2y^2 + 12y + 36 - 26 = 0

    2y^2 + 12y + 10 = 0

    y^2 + 6y + 5 = 0

    y^2 + y + 5y + 5 = 0

    y (y + 1) + 5 (y + 1) = 0

    (y + 1) (y + 5) = 0

    Then

    y + 1 = 0

    y = - 1

    so x - y = 6

    x + 1 = 6

    x = 5

    Or

    y + 5 = 0

    y = - 5

    Again x = 1

    So the solutions would be (-1, 5), (1, - 5). The correct option is option "C".
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