Is this nonlinear equation solvable?

[pyroknife]

The 3 equations are:
3xy-2xz=-1,
-xy-xz=-1,
-2xy+3xz=2

I've never learned how to solve these nonlinear equations. Is there anyway to solve this?
I tried wolframalpha, but this was the result:
http://www.wolframalpha.com/input/?i=3xy-2xz=-1,+-xy-xz=-1,+-2xy+3xz=2

 

[micromass]

Substitute a=xy and b=xz and solve the linear system.

Another way you can do it is by factoring out x.

 

[antibrane]

It is giving you a solution,
$$y=\frac{1}{5x}\qquad z=\frac{4}{5x}$$
In fact that is an infinite number of solutions, since $x$ is just a free-parameter. You get this because not all of your equations are independent. In other words, one of the equations can be written as a linear combination of the other two.