It's a 100% standard problem in any basic physics course, and I cannot solve it.
Here's the scenario:
What is the tension in the strings (T1 and T2)?
My thoughts were (cos/sin rewritten as cos(60°)=½ or cos(45°)=½√2, for example):
From the x components:
cos(45°) T2 + cos(60°) T1 = 0
T1 = −√2 T2
From the y components:
sin(60°) T1 + sin(45°) T2 = m g
½√3 T1 + ½√2 T2 = m g
But using that as the basis to algebraically get the Ts leads to the wrong solution.
PS: Yes that's a homework (this edX course), but I already have the accepted solution (there is a "Show answer" button when one has exhausted ones attempts), and after this I'll drop the course anyway because it just takes too much time and I'm taking it just for fun.