How many solutions does this system have? Why is the solution and explain why?

Question

6x + 4y + 2z = 32

3x - 3y - z = 19

3x + 2y + z = 32

 

Answer 1

It has no solutions because the 1st equation is almost double the 3rd, except for the 32. If we were to eliminate the variables by multiplying the 3rd equation by -2...

 

6x + 4y + 2z = 32

-6x - 4y - 2z = -64

0 = -32

 

Well, that's not true at all.