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Math

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Solve the system using any algebraic method.
2x - 2y + z = 3
5y - z = -31
x + 3y + 2z = -21
______________________
The answer I got for this is ( -26, 6,67) but I know its wrong and I don't know why. Help please >< my work is at the bottom

I used substitution method changed 5y-z=-31 to z=5y+31 then I:
Plugged it in the first equation=
2x-2y+5y+31=3 -> 2x+3y+31=3 -> 2x+3y=-28 is my new 1st equation...
Plugged in z=5y+31 to equation 3 =
x+3y+2(5y+31)=-21 -> x+3y+10y+62=-21 -> x+13y+62=-21 -> x+13y=-83 is my new 2nd equation.
2(=13y=82)+3y=-28 -> -26-166+3y=-28 -> -23y=138 - > y=6
2x+3(6)=-28 -> 2x+18=-28 -> 2x=-46 -> x=-23
2(-26)-2*6)+z=3 -> -52-12+z=3 -> -64+z=3 -> z=67

  • Math -

    5y - z = -31

    z = 5y + 31



    2x - 2y + z = 3

    ( Now put z = 5y + 31 in equation )

    2x - 2y + 5y + 31 = 3

    2x + 3y = 3 - 31

    2x + 3y = - 28

    2x = - 28 - 3y Divide both sides with 2

    x = - 14 - ( 3 / 2 ) y



    x + 3y + 2z = -21

    ( Now put x = - 14 - ( 3 / 2 ) y and z = 5y + 31 in equation )

    - 14 - ( 3 / 2 ) y + 3y + 2 ( 5y + 31 ) = - 21

    - 14 - ( 3 / 2 ) y + 3y + 10y + 62 = - 21

    - ( 3 / 2 ) y + 13y = - 21 + 14 - 62

    - ( 3 / 2 ) y + ( 26 / 2 ) y = - 69

    ( 23 / 2 ) y = - 69 Multiply both sides with 2

    23y = - 138 Divide both sides with 23

    y = - 6



    z = 5y + 31

    z = 5 ( -6 ) + 31

    z = - 30 + 31

    z = 1



    x = - 14 - ( 3 / 2 ) y

    x = - 14 - ( 3 / 2 ) -6

    x = - 14 + 18 / 2

    x = - 14 + 9

    x = - 5


    So solutions are :

    x = - 5

    y = - 6

    z = 1

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