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algebra 2

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how do you solve
2x-y=7
-x+2y=-5 please show how you got this problem ! Thank you

  • algebra 2 -

    There are a couple of ways.

    First, the top equation says that y = 2x-7.
    So, substitute that into the bottom equation:

    -x + 2(2x-7) = -5
    -x + 4x - 14 = -5
    3x = 9
    x=3
    y=2x-7=6-7 = -1

    Another way is to remember that whole equations can be added and subtracted with each other, to give new equations. The goal of this method is to eliminate one or more variables by combining equations.

    This also relies on the fact that multiplyiong each term of an equation does not change the truth of the statement.

    So, multiply the bottom equation by 2 and then add the top equation:

    -2x + 4y = -10
    2x - y = 7

    Doing this yields

    0x + 3y = -3
    so, y = -1

    Now, plug that value into either of the original equations to see that x=3.

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