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12 February, 20:58

This system has one solution. {y=5x-9y=x2-3x+7 What is the y-coordinate of the solution?

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  1. 12 February, 21:06
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    The y-coordinate of the solution is 11.

    Both equations have y isolated. We will use substitution for this system:

    5x-9=x²-3x+7

    We want to gather all of the variables on one side, so we will subtract 5x from each side:

    5x-9-5x=x²-3x+7-5x

    -9=x²-8x+7

    We want the equation to be equal to 0 to solve it, so we will add 9 to both sides:

    -9+9=x²-8x+7+9

    0=x²-8x+16

    This is easy to factor; factors of 16 that sum to - 8 are - 4 and - 4:

    0 = (x-4) (x-4)

    Since these are the same factor, we solve it to get our answer:

    x-4=0

    x-4+4=0+4

    x=4

    Substitute this into the first, linear, equation:

    y=5 (4) - 9=20-9=11
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