# System of Equations

1. Jan 17, 2013

### jgreen520

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

Thanks

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2. Jan 17, 2013

### SammyS

Staff Emeritus

Do you mean F2B ?

If so, F2B has no defined meaning with what is given.

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

3. Jan 18, 2013

### jgreen520

So the part Im 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

4. Jan 18, 2013

### 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.

5. Jan 18, 2013

### SammyS

Staff Emeritus
FB∙2 + FB∙5​

that is equivalent to
FB(2 + 5)

which is 7∙FB .​

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

6. Jan 18, 2013

### vela

Staff Emeritus
$x = y$ 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?

7. Jan 19, 2013

### 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!