# Basic algebra question

1. Jul 17, 2006

### PhysicsApprentice

basic algebra question plz help :(

when combining the two equations

Vb-0.5FAC = 10
Hb -0.866FAC = -2

It brings the answer 1.732Vb - Hb = 19.32

2. Jul 17, 2006

### Office_Shredder

Staff Emeritus
You have Vb, Hb, and FAC as variables with only two equations?

Of course you're not going to solve it. Do these variable stand for something significant? Perhaps there is a third equation that you're missing

3. Jul 17, 2006

### sdekivit

They substituted FAC from the first equation into the second one. Now try to find this answer yourself.

4. Jul 17, 2006

### PhysicsApprentice

the answer i got myself was
1.732Vb - Hb = 12

i got no idea how they got 19.32

5. Jul 17, 2006

### sdekivit

did you came up with FAC = -20 + 2Vb ?

6. Jul 17, 2006

### PhysicsApprentice

yes that is correct

there is actually a third equation that when combined with the first two equations gives all the answers

the third equation is
2Vb - 3Hb = -26

Vb = 26.2
Hb = 26.1
FAC = 32.4

The problem i have is that i dont understand how the first two equations combined together gave the answer of 1.732Vb - Hb = 19.32

if you could write down the step by step procedure on how this answer came about it would be greatly appreciated.

7. Jul 17, 2006

### sdekivit

i won't write down all my steps because it's not allowed. Here is how you get to the equation that leads to 1,732Vb - Hb = 19,32:

From equation 1 it follows that:

$$FAC = \frac {(10-Vb)} {-0,5} \ = -2 (10-Vb) = -20 + 2Vb$$

This can be put in the second equation:

$$Hb -0.866(-20 + 2Vb) = -2$$