Determine whether the given system has only one solution, no solution, or infinite # of solutions. If the solution has only one solution, enter the solution
6x-4y+4z=4
4x+2y+6z=5
5x-y+5z=-2

Question

Determine whether the given system has only one solution, no solution, or infinite # of solutions. If the solution has only one solution, enter the solution
6x-4y+4z=4
4x+2y+6z=5
5x-y+5z=-2

radar · Answer

6x-4y+4z=4
8x+4y+12z=10 (2nd equation doubled) now add getting
14x+16z=14   y has been eliminated.  Now eliminate y again

4x+2y+6z=5
10x-2y+10z=-4 (last equation doubled)  now add
14x +16z =1
Note that 14x+16z =1 but we have shown 14x+16=14   So it is inconsistent.  I don't believe there is a solution.

anonymous · Answer

CORRECT

radar · Answer

Did you come to the same conclusion?

anonymous · Answer

yes

radar · Answer

Very good.

precal · Answer

I also, came up with the same solution with my trusty TI-84