Solving system of 3 equations

Two out of the 3 equations have 3 variables , one of the equations only has 2 variables. Help! I have no idea what to do!
The problem is
-6x+5y+z=12
-4x+3y=6
2x-4y+4z=-18

Question

Solving system of 3 equations 

Two out of the 3 equations have 3 variables , one of the equations only has 2 variables. Help! I have no idea what to do! 
The problem is 
-6x+5y+z=12
-4x+3y=6
2x-4y+4z=-18

anonymous · Answer

The one with only 2 variables...add a 0z

anonymous · Answer

Take the first two equations. I'm going to eliminate the x values.
2(-6x+5y+z=12)       -12x+10y+2z=24
-3(-4x+3y =6)            12x-9y         =-18   
                                             y+2z=6   save this for later

anonymous · Answer

Now take the last two equations. I'll eliminate x againl
-4x+3y     =6               -4x+3y     =6      
2(2x-4y+4z=-18)          4x-8y+4z=-36
                                          -5y+4z=-30     save this for later

anonymous · Answer

take the two saved equations and eliminate a variable...Im going to eliminate y
 y+2z=6        5(y+2z=6)        5y+10z=30
-5y+4z=-30                         -5y+4z=-30
                                                    14z=0
                                                        z=0
Solve for x and y now.