Why are there five equations? It takes three equations to allow you to solve for x, y and z. If you have more equations the additional ones are either (a) redundant or (b) inconsistent. Here if you solve for x, y, and z using the first three equations you get x= 1, y = -2 and z = 3. This solution also works for the 4th equation, but it doesn't work for the fifth - therefore the fifth equation is not consistent with the other four. Here's a simple example that may make it clearer - suppose you are give two equations with unknowns x and y:x+y = 2x = 1It's easy to see that y must equal 1. But suppose I throw in a third inconsistent equation:x+y=2x=1y=100Clearly it can't be that all three equations are true. This is what's happening with the 5 equations as you've written them. However, I wonder if there's a typo in your fifth equation? If it was 3x+3y+2z=3 then it would be consistent with the others (note the 3y term instead of 2y).