Question 770111
3x+2y-2z=14....(1)
2x-5y+3z=7.....(2)
4x-3y+7z=5.....(3)
Multiply (1) by 2
Multiply (2) by 3
6x + 4y - 4z = 28....(1)
6x - 15y +9z = 21.....(2)
Subtract:
     19y - 13z = 7  Equation A
Multiply (2) by 2
4x - 10y + 6z = 14....(2)
Subtract (3)
4x - 10y + 6z = 14....(2)
4x - 3y + 7z = 5......(3)
Subtract
     -7y - z = 9 Equation B
......................
Consider Equations A and B
19y - 13z = 7.....(A)
-7y - z   = 9.....(B)
Multiply (B) by 13 and 
subtract from (A)
19y - 13z = 7.....(A)
-91y - 13z = 117...(B)
110y       = -110
   y = -1.
Substitute y = -1 into
Equation A
19y - 13z = 7.....(A)
19(-1) - 13z = 7
-19 - 13z = 7
   -13z = 7 + 19
   -13z = 26
      z = -2
..................
Substituting y = -1 and z = -2
into Equation 1
3x+2y-2z=14....(1)
3x + 2(-1)-2(-2) = 14
3x -2 + 4 = 14
3x       = 14 - 2
3x       = 12
x        = 4.

x = 4, y = -1, z = -2
Hope this helps.
:-)