As part of a question on axial load I need to simplify two equations in terms of P ([1] and [2]). In the above you can see how F_{BA} and F_{BC} were simplified to 0.8081P and 0.7143P respectively. I understand both the section prior to this and the one after, though I do not understand how this simplification was carried out. Any help would be greatly appreciated. Thanks.
You have a system of equations of the form \begin{align} ax+by&=0\\ cx+dy+e&=0 \end{align} The trick to find x and y is always to add a multiple of one equation to the other so that either x and y is eliminated. (In this case, you can e.g. add -a/c times the second equation to the first equation). Then you have an equation with only one variable, and you can easily find its value. Repeat the procedure for the other variable.