What is the solution of the system of equations?-3x-4y-3z=-72x-6y+2z=35x-2y+5z=9

If you have a TI-83 plus or higher, you could create a matrix and use rref to get the solution.

Let's begin with eliminating the y's in equations 1 and 3, then in equations 2 and 3:
[tex]-3x-4y-3z=-7 [/tex] times -1⇒ [tex]3x+4y+3z=7 [/tex] 
[tex]5x-2y+5z=9[/tex] times 2⇒ [tex]10x-4y+10z=18[/tex]

ADD the two equations: 13x + 13z = 25

[tex]2x-6y+2z=3[/tex] times -1⇒[tex]-2x+6y-2z=-3[/tex]
[tex]5x-2y+5z=9[/tex] times 3⇒ [tex]15x-6y+15z=27[/tex]

ADD the two equations: 13x+13z=24

Subtract the two resulting equations and you get 0 = 1 which is false so there is no solution  for the system.