Solve the system using any algebraic method.

Question

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

Answer 1

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