Solving systems with 3 equation

Question

If x + y + z = 10, x - y - 2z = -14, and x + z = 6

then x =

I got x = 2/3

my teacher said during class to use elimination and substitution. I'm not sure if I did it right. If anyone can verify it that would awesome!

Answer 1

x+y+z = 10

x-y-2z = -14

x + z = 6

Eliminates y by adding Equation#1 PLUS equation #2:

2x - z = -4

The resulting 2x2 is:

2x - z = -4

x + z = 6

adding these: 3x = 2

x = 2/3, so yes you are correct..

per 3rd equation: 2/3 + z = 6

2 + 3z = 18

3z = 16

z = 16/3

Per 1st equation: 2/3 + y + 16/3 = 10

y + 6 = 10

y = 4

check: 2nd equation: x - y - 2z = 2/3 - 4 - 32/3 = -4-10 = -14

3rd equation: x+z = 2/3+16/3 = 18/3 = 6

x = 2/3, y = 4, z = 16/3