How to solve a system of equations I have this system of equations:
3x²+7y²=55
and
2x²+7xy=60
Is there a method of solving [x,y] without using x²=t, y²=z?

Yes, since $x$ is nonzero (because of the second equation), we can eliminate
$y=(60-2x^2)/(7x)$ and substitute this in the first equation, which gives
$$
25(x + 4)(x + 3)(x - 3)(x - 4)=0.
$$
