BRAIN WORKS ~1

My solution uses calculus. I'm interested to see what other solutions people come up with--as I am the first to post a solution. I started by solving for $z$ in the first equation (i.e. $z=5-x-y$ ), and substituting it into the second equation. After simplification, I get $5y-y^2+5x-x^2-xy=3$ . Then, differentiating with respect to $y$ ... $5-2y+5\frac{dx}{dy}-2x\frac{dx}{dy}-\frac{dx}{dy}y-x=0$ . Setting $\frac{dx}{dy}=0$ , I get $y=\frac{5-x}{2}$ . Substituting that into $5y-y^2+5x-x^2-xy=3$ , and solving for $x$ , I get $x=-1,13/3$ .