Statics machine equilibrium: support reaction- I have too many unknowns

[musicmar]

Please help Due in 2 hours. Statics machine equilibrium: reactions- too many unknowns

Homework Statement

The woman using the lat pulldown machine is holding the 80-lb weight stationary in the position shown. What are the reactions at the built-in support E and pin support F? (A and C are pinned connections)

The Attempt at a Solution

First, I isolated the pulleys and rope to find the components of the tension at D.
D_x=80cos60=40 lb
D_y=-40√3 lb

Then I set up my three equilibrium equations:

∑M_E=0= -(80 lb)(13/6 ft) - (40√3 lb)(17/3 ft) - (40 lb)(27/4 ft) + M_E + F_y(25/6 ft)

M_E= (680√3)/3 +1330/3 + (25/6)F_y

∑F_x= 0 = E_x + F_x + (40 lb)

∑F_y= 0 = E_y + F_y - (80 lb) - (40√3 lb)


Right now, I have 3 equations and 5 unknowns, E_x, E_y, M_E, F_x, and F_y.

I'm probably supposed to break it up into two systems, first just the top portion. But I'm not really sure how to proceed from here.

Thank you!

 

[musicmar]

Please help. Due in 45 minutes.