Part of my textbook is dealing with suspension block problems with 2 vectors and a weight which sums to 0.(R+S+W=0)

The two angles where the vector meets the 350lb load are 55 and 37 degrees from a supposed x-axis.(W=350)(180-55=125)

I follow along up to this part and can't seem to substitute to solve for this system:

Solving the system gives you the answers ~280 and 201

How do you solve the system?