Alg2

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Solve the system for z.
2x - y + 2z = 11
x - 2y - 3z = -5
-3x + z = -3

  • Alg2 -

    - 3 x + z = - 3 Add 3 x to both sides

    - 3 x + 3 x + z = - 3 + 3 x

    z = 3 x - 3


    x - 2 y - 3 z = - 5

    x - 2 y - 3 * ( 3 x - 3
    ) = - 5

    x - 2 y - 3 * 3 x - 3 * ( - 3 = - 5

    x - 2 y - 9 x + 9 = - 5

    - 8 x - 2 y + 9 = - 5 Add 8 x - 9 to both sides

    - 8 x - 2 y + 9 + 8 x - 9 = - 5 + 8 x - 9

    - 2 y = - 14 + 8 x Divide both sides by - 2

    y = - 14 / - 2 + 8 x / - 2

    y = 7 - 4 x


    2 x - y + 2 z = 11

    2 x - ( 7 - 4 x ) + 2 * ( 3 x - 3 ) = 11

    2 x - 7 + 4 x + 6 x - 6 = 11

    12 x - 13 = 11 Add 13 to both sides

    12 x - 13 + 13 = 11 + 13

    12 x = 24 Divide both sides by 12

    x = 24 / 12

    x = 2


    y = 7 - 4 x

    y = 7 - 4 * 2

    y = 7 - 8

    y = - 1


    z = 3 x - 3

    z = 3 * 2 - 3

    z = 6 - 3

    z = 3


    Solution :

    x = 2 , y = - 1 , z = 3

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