Well this is awkward. I've been through three semesters of calculus and yet this system of linear equations is causing me to brain fart.
$$\begin{align*} &&3y&=4x\\ &&2x+3z&=4y\\ 2x+y+z=4z &\to& 2x+y&=3z\\ &&x+y+z&=1 \end{align*}$$
I can obviously just get the answer with Wolfram Alpha, but I'm really bugged that I can't figure this out. All I've been able to do is fudge around terms and I'm not getting anywhere.