# Thread: Solve for two Variables using substitution

1. ## Solve for two Variables using substitution-Help

I have been working on homework and cant seem to grasp the right order or equation movements in.

AN example of a question would be

SOlve for both FB and FA using substitution

Given:

-FA cos(35) + FB cos(75)=0
-FA sin(35) +FB sin(75)= 235.4

Any help would be appreciated

THis is my work

-FA cos(35) +FBcos(75)=0
FB=FAcos(35)/cos(75)
substitute
-FAsin(35)+(FAcos(35)/cos(75))sin(75)=235.4

and then whatever i try seems to make no sense after that. I may be missing a rule or something but if any have explanations that would be awesome.

2. ## Re: Solve for two Variables using substitution-Help

Originally Posted by gramgilb
-FA cos(35) + FB cos(75) = 0
-FA sin(35) + FB sin(75) = 235.4
U = FA, V = FB
a = cos(35), b = cos(75)
c = sin(35), d = sin(75)

-Ua + Vb = 0 [1]
-Uc + Vd = 235.4 [2]

[1]: V = Ua / b ; substitute:
[2]: -Uc + Uad / b = 235.4
Multiply by b:

U = 235.4b / (ad - bc)

Can you wrapper up now?

Fa=
Fb=

4. ## Re: Solve for two Variables using substitution-Help

kk i understand now i was only multiplying b to the other side thanks for the help

5. ## Re: Solve for two Variables using substitution-Help

Originally Posted by gramgilb
kk i understand now i was only multiplying b to the other side thanks for the help
Well, betya you'll never do that again!
So you should get:
U = FA = 94.78403....
V = FB = 299.98772...