How can I find Y from two equations WITHOUT using X?

[danni7070]

How can I find Y from two equations WITHOUT using X:

(1) Xcos(Z) - Ycos(W) = 0

(2) Xsin(Z) + Ysin(W) - mg = 0

Now I have found out that

Y = Xcos(Z) / cos(W) and also

Y = mg - Xsin(Z) / sin(W)

How can I eliminate X from these two equations ??

Me algebra isn't good...

 

[AlephZero]

I hope you meant

Y = (mg - Xsin(Z)) / sin(W)

the extra brackets are important!

It's easy to eliminate Y from the two equations you got.

Xcos(Z) / cos(W) = (mg - Xsin(Z)) / sin(W)

But you wanted to eliminate X, not Y. So start again and rearrange the two equations as

X = ...

not as Y = ...

 

[arildno]

Rewrite your first equation as:
Xcos(z)=Ycos(w)

Does any bell ring for you?
Some manipulation you may make to solve for X, in terms of Y, w and z?

 

[danni7070]

Well, I'm trying to eliminate X frome (1) and (2) so I can solve Y in terms of anything BUT X.

I'm sorry but Xcos(z)=Ycos(w) doesn't ring any bell for me

 

[arildno]

Well, as long as Cos(z) does not equal 0, we have:
$$X=Y\frac{\cos(w)}{\cos(z)}$$

Thus, inserting this on the X's place in your second equation, you get:
$$Y\cos(w)\tan(z)+Y\sin(w)=mg$$
whereby you get:
$$Y=\frac{mg}{\cos(w)\tan(z)+\sin(w)}$$

 

[danni7070]

Ok! That was the simple rule I was looking for! Ycos(w)/cos(z) = Ycos(w)tan(z)

Thank you very much!