x + y+2z = 7 ------> y = 7 -x-2z (a)
2x - 3y -2z = -4 (d)
x -z = -2 ------> x=-2+z (b)
Substitute x(from the equation b) to the equation (a).
y = 7 -x-2z = 7 -(-2+z) -2z = 7 +2 -z - 2z= 9 - 3z
y=9 - 3z (c)
(b) and (c) substitute into (d)
2x - 3y -2z = -4
2(-2+z) -3(9-3z)-2z = -4
-4+2z-27+9z - 2z =- 4
9z= 27
z= 3
x=-2+3,
x=1
y = 7 -x-2z =7-1-2*3 = 0
y=0
Answer: x=1, y=0, z=3.
Check:
1) 2x - 3y -2z = -4
2*1 - 3*0 -2*3 = -4
-4=-4
2)x + y+2z = 7
1+0+2*3=7
7=7
3) x-z=-1
1-3=-2
-2=-2