Tension Problem x and y components??

[Span]

1. The problem statement, all variables and given/known data

A man of mass 70.0 kg hangs by 2 cables A and B each inclined at 60.0 degrees to the horizontal.

A horizontal pulling force F is applied to the man pulling to the right. The man remains stationary. If F has magnitude 250 N, find the magnitudes of the tension in the 2 cables.


2. Relevant equations

F=w=mg
A+B+F+W=0



3. The attempt at a solution

(70 kg)(9.8)=686 N
the downward W force is 686 N

x-component
Ax+Bx+F=0
Acos120+Bcos60+250=0

y-component
Ay+By+W=0
Asin120+Bsin60+686=0

I know there is a system of equations here and that i can use substitution or trigonometric triangles but im not sure how to approach either of these methods. Any help would be great. Sorry i don't have a picture, i hope it makes sense.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Astronuc]

Acos120+Bcos60+250=0
Asin120+Bsin60+686=0

Evaluate the cos and sin terms, and one has two equations and two unknowns, which one should be able to solve.

[Span]

hmm sorry it still doesnt make sense to me im not sure how to put B in terms of A or A in terms of B and then after i find these numbers how to go about finding the tensions of the cables.

[Chi Meson]

First of all the weight is negative (sin270, right?)

Now turn all those sins and cos's into decimals, and rewrite the first equation so that it reads " A = blablablah + B(blah)"

then substitute that for the "A" in the second equation.