geometry honors

Can you prove ABCD is a parallelogram based on the given information? Explain.
Given: x = 5, y = 4
Prove: ABCD is a parallelogram.

The image consists of a quadrilatera ABCD with their sides AB, BC, CD, DA as 3x + 12, 7y - 8, 6x - 3 and 5y respectively.

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  1. To be a ||gm , opposite sides must be equal
    7y-8 = 5y and 6x-3 = 3x+12

    7y - 8 = 5y
    2y = 8
    y = 4

    6x-3 = 3x+12
    3x = 15
    x = 5

    Since the given information about x and y match those solutions, yes, it is a parallogram

    or

    just sub in the given values into the 4 different expressions to see that indeed opposite sides are equal

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