I have an example and a problem i am working on. The example is as follows: There are three strings. One hangs down with 100N while of the other two one goes up to the right from the equilibrium point at 45 degrees and the other goes left. I believe this set of Rx and Ry vector components is solving through the algebra method of linear equations. The string going up and to the right has an x and y component. The string going sideways only has an x component. Due to the simplicity of this problem it is possible to solve for the tension of the string going up by simply moving 100N to the other side and taking sin 30 and then moving it under 100N. This is put in the component of the horizontal string. This string is simply T1 cos 30. This gives us T3. The problem i am working on gives three string tensions and three weights. I solved for the first two weights and the first two tensions. The remainder of the problem is drawn as follows: An equilibrium point with a weight hanging on it of unknown value N. The right string is attached to the wall at 50 degrees and the left string goes up and over a pulley leaving from an angle of 30 degrees. It was already solved that the tension of the left string is 14.1 (there are 20 N coming from that side at equilibrium in another point). This is not a simple problem where you can just solve for one string at a time because you do not know the weight N. In the book example you could do this. I believe that the way to solve this problem is to set up one whole x component for all forces represented and then a y component for the whole thing. You then put one into the other. This gives: 0 = Rx = 14.1N - T3Cos 50 - ?N 0 = Ry = 14.1N - T3Sin 50 - 20N (This component system has 14.1 as T1 coming from the left and T3 as the unknown string going up to the right) I put 20N on the y axis because it is pulling on the left string (theres 20N in equilibrium coming from there) and 'unknown # Newtowns' on the x axis because it is hanging down from the equilibrium point which we are solving for. In the book example if was possible to isolate N and solve everything against it. Here we have two Newton values and we do not know one of them. I am trying to solve this like a system of linear equations by isolating for N and finding everything from it. I cannot find a way to merge the two N values however. What is the trick to solving for the sum N so that i can find all the other tensions from it? Is this the same type of problem where you solve for one T off of N and then plug it into the other or is this a different type of math? If it is a different type of math where do i look in lower level math or trig or calc to find it? Thanks.