How to find x and y in this vector question if P is in equilibrium?

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picture of the diagram

This is what i tried: sum of upward forces= sum of downward forces

x sin 90 + y sin 60 - 8 sin 30

x sin 90 + y sin 60 - 4

sum of forces to the right= sum of forces to the left

7 + x cos 90 - y cos 60 - 8 cos 30

7 + x cos 90 - y cos 60 - 6.93

x cos 90 - y cos 60 + 1.93

and i lost myself here....please help!

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You're on the right track. One possible reason why you're stuck is because your solution is poorly formatted.

A loose definition of equilibrium in $\mathbb{R}^2$ is if $\Sigma \overrightarrow{f_x}=0$ and $\Sigma \overrightarrow{f_y}=0$. Knowing this:

\begin{align} \Sigma \overrightarrow{f_x}=0&=7-y\cos60^{\circ}-8\cos30^{\circ}\\ 0&=7-\frac12y-4\sqrt3\\ \Sigma \overrightarrow{f_y}=0&=x+y\sin60^{\circ}-8\sin30^{\circ}\\ 0&=x+\frac{\sqrt3}{2}y-4\\ \end{align}

You now have two equations with two variables. Can you take it from here?