why does this system cannot be solved?

2x + 2y + 3z = 23
2x + 2y + 5z = 33
-4x - 4y - 8z = -55

Question

why does this system cannot be solved?

2x + 2y + 3z = 23
2x + 2y + 5z = 33
-4x - 4y - 8z = -55

anonymous · Answer

Subtract first equation from second equation gives 2z = 10 or z = 5.
If you multiply the first equation by 2 and add it to the third equation, you get -2z = 9 or z = -9/2.  We have two different values for z, so the system can not have a solution.

anonymous · Answer

No, I mean, there is a way that allows me at first glance to figure out that this equation has not a solution?

anonymous · Answer

Add the first 2 equations and multiply the result by -1.  You get -4x -4y -8z = -56, but the third equation is -4x -4y -8z = -55

anonymous · Answer

lol, I misunderstood a question before so I thought there was a simple way to see if one system has/has not a solution. I know how to solve that system. Thank you very much djvu