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March 29, 2017

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Solve

2x-y-5z=1
x+2y+3z=9
3x+6y+z=11

2x-3y=-13
-5x+2y=16

  • Math Help!! - ,

    1. Eq1: 2x -y - 5z = 1.
    Eq2: x + 2y + 3z = 9.
    Eq3: 3x + 6y + z = 11.
    Multiply Eq1 by 3 and Eq2 by 5:
    6x - 3y -15z = 3
    5x + 10y + 15z = 45
    Add Eq1 and Eq2:
    Eq4: 11x + 7y = 48

    Eq2: x + 2y + 3z = 9
    Multiply Eq3 by -3:
    Eq3: -9x - 18y - 3z = -33
    Add Eq2 and Eq3 and get:
    Eq5: -8x - 16y = -24
    Eq5: -x - 2y = -3

    Eq4: 11x + 7y = 48
    Eq5: -x - 2y = -3.
    Multiply Eq5 by 11 and add to Eq4:
    Eq5: -11x - 22y = -33
    -15y = 15
    Y = -1.
    In Eq5, substitute -1 for y:
    -x - 2*(-1) = -3
    -x + 2 = -3
    -x = -5
    X = 5.
    In Eq1, sub. 5 for X and -1 for Y:
    2*5 - (-1) - 5z = 1
    10 + 1 - 5z = 1
    -5z = 1 - 11 = -10
    Z = 2.
    Solution set = (x,y,z) = (5,-1,2).

    2. Eq1: 2x - 3y = -13.
    Eq2: -5x + 2y = 16.
    Multiply Eq1 by 5 and Eq2 by 2:
    10x - 15y = -65.
    -10x + 4y = 32.
    Add the 2 Eqs:
    -11y = -33
    Y = 3.

    In Eq1, substitute 3 for Y:
    2x - 3*3 = -13
    2x = -13 + 9 = -4
    X = -2.
    Solution set = (-2,3).

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