Simplifying Basic Algebra Equations: An Explanation and Example

[PhysicsApprentice]

basic algebra question please help :(

when combining the two equations

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

It brings the answer 1.732Vb - Hb = 19.32


can someone plx explain to me how this answer came about

 

[Office_Shredder]

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

 

[sdekivit]

when combining the two equations

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

It brings the answer 1.732Vb - Hb = 19.32


can someone plx explain to me how this answer came about

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

 

[PhysicsApprentice]

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

i got no idea how they got 19.32

 

[sdekivit]

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

i got no idea how they got 19.32

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

 

[PhysicsApprentice]

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

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


the final answers are

Vb = 26.2
Hb = 26.1
FAC = 32.4



The problem i have is that i don't 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.

 

[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:

[tex] FAC = \frac {(10-Vb)} {-0,5} \ = -2 (10-Vb) = -20 + 2Vb [/tex]

This can be put in the second equation:

[tex]Hb -0.866(-20 + 2Vb) = -2 [/tex]

This will deliver your asked formula when properly worked out.

 

[PhysicsApprentice]

thank you so much

i swear to god if i had a credit card i would pay you 5 dollers