Solving the General Equilibrium with $4$ equations and $4$ unknowns

Question

I have to solve four equations to solve the equlilibrium prices for the two countries:

1. $\frac{2p_1}{w_1} + \frac{p_1}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_1w_1}+ \frac{48w_2^2+p_1^2+4p_2^2}{8p_1w_2}$
2. $\frac{p_2}{2w_1} + \frac{2p_2}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_2w_1}+ \frac{48w_2^2+p_1^2+4p_2^2}{8p_2w_2}$
3. $48w_1^2=4p_1^2+p_2^2$
4. $48w_2^2=4p_2^2+p_1^2$

I have set $w_2=1$ and that leaves me with four equations and three unknowns. However, it is still very hard to solve for the $p_1$,$p_2$, and $w_1$ (we already know that $w_2=1$). On paper, I have a plethora of substitutions and sub-equations going on, but I don't think I am going anywhere with it, and so need some professional advice.

Edit: Is there a way for me to use Maple to solve this system of equations?