# Solving a System of Equations: Understanding F_B

• jgreen520
In summary, the equation in the question has x and y on opposite sides of the equation and you don't add them.
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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jgreen520 said:
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 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.

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

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.

jgreen520 said:
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
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 $\displaystyle \ \ F_B\left(\sin(45^\circ)+\frac{\cos(45^\circ)}{\sin(45^\circ)+\cos(45^\circ)\tan(31.964^\circ)}\right)\ .$

jgreen520 said:
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?

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!

## What is a system of equations?

A system of equations is a set of two or more equations with multiple variables that are all related to each other. The goal is to find the values of the variables that satisfy all of the equations simultaneously.

## What is the purpose of solving a system of equations?

The purpose of solving a system of equations is to find the values of the variables that make all of the equations true. This can help to solve real-world problems, as well as provide a deeper understanding of mathematical concepts.

## What is the difference between a consistent and an inconsistent system of equations?

A consistent system of equations has at least one solution that satisfies all of the equations, while an inconsistent system has no solution that satisfies all of the equations. In other words, a consistent system has a solution that makes all of the equations true, while an inconsistent system has no solution that makes all of the equations true.

## What methods can be used to solve a system of equations?

There are several methods for solving a system of equations, including substitution, elimination, and graphing. These methods involve manipulating the equations algebraically or visually to find the values of the variables that satisfy all of the equations.

## How can solving a system of equations be applied in the real world?

Solving a system of equations can be applied in many real-world situations, such as in economics, engineering, and physics. For example, it can be used to find the optimal solution for a business problem or to determine the intersection point of two moving objects.

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