One method would be to just replace "sin(37)" with 0.6018, "cos(37)" with 0.7986, sin(125) with 0.8191, and cos(125) with -0.5736 to get -0.5736|R|+ 0.7986|S|= 0 and 0.8191|R|+ 0.6018|S|= 350. Now, for example, multiply each term in the first equation by 0.8191 each term in the second equation by 0.5736 so that the "|R|" terms in the equations are -0.5736)(0.8191)|R| and (0.8191)(.5736)|R| so that now adding the two equations will eliminate |R| leaving a single equation for |R|.

Another method, since you mention not being able to substitute, is to write the first equation as |R|cos(125)= -|S|cos(37) so that and replace |R| in the second equation by that. Of course, eventually, you will have to replace sin(37), cos(37), sin(125), and cos(125) by their numerical values.