X+y+z=2

x+2y-z=5

2x+y-z=5

Answer: [3] x = 2y - 3z - 6

/ / Plug this in for variable x in equation [1]

[1] (2y-3z-6) + y + z = 2

[1] 3y - 2z = 8

/ / Plug this in for variable x in equation [2]

[2] 2• (2y-3z-6) + y - z = 5

[2] 5y - 7z = 17

/ / Solve equation [2] for the variable y

[2] 5y = 7z + 17

[2] y = 7z/5 + 17/5

/ / Plug this in for variable y in equation [1]

[1] 3• (7z/5+17/5) - 2z = 8

[1] 11z/5 = - 11/5

[1] 11z = - 11

/ / Solve equation [1] for the variable z

[1] 11z = - 11

[1] z = - 1

/ / By now we know this much:

x = 2y-3z-6

y = 7z/5+17/5

z = - 1

/ / Use the z value to solve for y

y = (7/5) (-1) + 17/5 = 2

/ / Use the y and z values to solve for x

x = 2 (2) - 3 (-1) - 6 = 1

Solution:

{x, y, z} = {1,2,-1}