Solving multiple linear equations I'm a bit rusty on my linear algebra.
I have the following equations:
$$\operatorname{weight}_C = \frac{\frac{P_y - A_y}{B_y - A_y} - \frac{P_x - A_x}{B_x - A_x}}{ \frac{A_x-C_x}{B_x-A_x} -  \frac{A_y-C_y}{B_y-A_y}};$$
$$\operatorname{weight}_B = \frac{P_x - A_x + \operatorname{weight}_C\cdot(A_x-C_x)}{B_x-A_x};$$
$$\operatorname{weight}_A = 1-\operatorname{weight}_B-\operatorname{weight}_C;$$
And I have values for all variables except $P_x$ and $P_y$.
How do I go about solving for $P_x$ and $P_y$ given the equations above?
Is it possible given this information?

You have two equations in two unknowns-the third has no unknowns in it.  Isolate $P_x$ in the second by multiplying by $B_x-A_x$ then adding the appropriate terms.  It should just be a number because you know everything else.  Then just put that into the first equation and solve for $P_y$
