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2 November, 03:55

How many solutions does this system have? 2x-4y=8 x+y=7

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  1. 2 November, 05:27
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    This system has one solution, which is x = 6 and y = 1.

    Step-by-step explanation:

    Solving by separation:

    Three cases:

    If we end up with cx (or cy) = d, in which c is different of zero, the system has one solution.

    If we end up with cx = d, in which c is zero and d is zero, the system has infinite solution.

    If we end up with cx = d, in which c is zero and d is not zero, the system does not have any solution.

    Solving this system:

    2x - 4y = 8

    x + y = 7

    So

    x = 7 - y

    Replacing in the first equation

    2 (7 - y) - 4y = 8

    14 - 2y - 4y = 8

    -6y = - 6

    6y = 6

    None of the coefficients are zero, so one solution

    y = 1

    x = 7 - y = 7 - 1 = 6

    This system has one solution, which is x = 6 and y = 1.
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