What is the solution to the system of equations? {-x+y+2z=7 { 2x-3y-2z=-4 { x -z=-2

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

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