Find the complete solution of the linear system.

Question

x - y + z = 0

y + 2z = -2

x + y - z = 2

Answer 1

x-y+z = 0

y +2z = -2

x+y-z = 2

add the 1st and last equations to eliminate y and z, leaving

2x = 2,

divide by 2

x=2/2 = 1

x= 1

plug that into the 1st equation: 1-y+z = 0,

y=z+1

plug that into the 2nd equation

y+2z = -2

z+1 +2z = -2

3z = -3

z = -1

y= z + 1 = -1 + 1 = 0

y =0

(x,y,z) = (1,0, -1)

check that with the 3rd equation:

x +y -z = 2

1 +0 -(-1) = 2

2= 2

solution is x= 1, y= 0, z=-1