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Math Help - system of equations

  1. #1
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    homework help please

    I need help solving these equations:
    x -4y = 6 2x+y-2z=-17 5x-y-2z=1
    2y +3z=1 x-3y+z=10 3x+4y+z=-2
    2x -z= 3 x+4y-2z=-23 2x+5y-z=-11

    system of equation with three varialbles
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  2. #2
    hpe
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    Quote Originally Posted by Panaboy
    I need help solving these equations:
    x -4y = 6 2x+y-2z=-17 5x-y-2z=1
    2y +3z=1 x-3y+z=10 3x+4y+z=-2
    2x -z= 3 x+4y-2z=-23 2x+5y-z=-11

    system of equation with three varialbles
    These are nine equations. Is each line a separate system?

    Here's how you can solve e.g. the first one:
    x -4y = 6 2x+y-2z=-17 5x-y-2z=1

    Solve the first equation for x: x = 6+4y

    Substitute into the other two:
    2(6+4y) + y -2z = 17 5(6+4y) - y - 2z = 1

    and simplify:
    12 + 8y + y -2z = 17 30 +20y - y -2z = 1

    which becomes
    9y - 2z = 5 19y - 2z = -29

    Solve the first of these for 2z (since this also appears in the second equation):
    2z = 9y - 5

    Substitute into the second one:
    19y - (9y - 5) = -29

    which becomes
    10y + 5 = -29

    Solve this for y, then use the bold equations to find z and x, and you are done.
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