Solve the system. x + 9y + z = 20
x + 10y – 2z = 18
3x + 27y + 2z = 58
Enter your answer as an ordered triple.

{x,y,z} = {-18,4,2}

Step-by-step explanation:

Solve equation [2] for the variable  x  

x = -10y + 2z + 18

Plug this in for variable  x  in equation [1]

(-10y+2z+18) + 9y + z = 20

- y + 3z = 2

Plug this in for variable  x  in equation [3]

 3•(-10y+2z+18) + 27y + 2z = 58

   - 3y + 8z = 4

Solve equation [1] for the variable  y  

 y = 3z - 2

Plug this in for variable  y  in equation [3]

  - 3•(3z-2) + 8z = 4

   - z = -2

Solve equation [3] for the variable  z  

 z = 2

By now we know this much :

 x = -10y+2z+18

   y = 3z-2

   z = 2

Use the  z  value to solve for  y  

 y = 3(2)-2 = 4

Use the  y  and  z  values to solve for  x  

 x = -10(4)+2(2)+18 = -18

b.

step-by-step explanation:

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