Solving a System of Equations: Understanding F_B

[jgreen520]

I was trying to understand why in the attached equations when they divided to get F_B alone it wasn't 2B.

Thanks

 

[SammyS]

I was trying to understand why in the attached equations when they divided to get F_B alone it wasn't 2B.

Thanks

Do you mean F_2B ?

If so, F_2B has no defined meaning with what is given.

What was done was that F_B was factored out of the two terms on the right-hand side of the first equation. --- F_B being a common factor.

 

[jgreen520]

So the part I am curious about is why when you have 2 F_b's or say they were x's do you just factor them out. Normally once you have each variable on opposite sides of the equation you add them. So if you had 5 different x's on one side of the equation you would just factor them out and not add them?

Thanks

 

[jing2178]

Same thing really

5x + 8x + 4x = 17x add the x's

5x + 8x + 4X =(5 + 8 + 4)x = 17x factorise the x and add

When the coefficients more complicated as in your question it is usual to factorise and in the example as given it shows the how the result was achieved.

 

[SammyS]

So the part I'm curious about is why when you have 2 F_b's or say they were x's do you just factor them out. Normally once you have each variable on opposite sides of the equation you add them. So if you had 5 different x's on one side of the equation you would just factor them out and not add them?

Thanks

So if you had

F_B∙2 + F_B∙5​

that is equivalent to

F_B(2 + 5)

which is 7∙F_B .​

Here you have $\displaystyle \ \ F_B\sin(45^\circ)+F_B\frac{\cos(45^\circ)}{\sin(45^\circ)+\cos(45^\circ)\tan(31.964^\circ)}$

which is equivalent to $\displaystyle \ \ F_B\left(\sin(45^\circ)+\frac{\cos(45^\circ)}{\sin(45^\circ)+\cos(45^\circ)\tan(31.964^\circ)}\right)\ .$

 

[vela]

So the part I am curious about is why when you have 2 F_b's or say they were x's do you just factor them out. Normally once you have each variable on opposite sides of the equation you add them. So if you had 5 different x's on one side of the equation you would just factor them out and not add them?

$x = y$ has variables on opposite sides of the equation. You don't add the x and y here.

$2x = 3x+3$ has x's on the opposite sides of the equation, but again, you don't add them.

Could you give an example of what you're talking about because it's not at all clear from what you've written?

 

[jgreen520]

After seeing the examples I see what I missed! Just factoring out the common term/coefficient. I was just missing it because the equation was a bit busy.

Thanks!