Linear eq. system solution?

[thomasvt]

I have a physical problem that I already turned into a system of equations:

q*t = c + x*t (1)
e*t = f + y*t (2)
x^2 + y^2 = g^2 (3)

I wanted to solve it, but the result gets complicated and I wonder if there is a simpler solution.
I basically solve for x from (3), use that in (1) to solve for y. Then I use that in (2) to solve for t:

(3) => x = sqrt(g^2 - y^2) (4)
use (4) in (1) => q*t = c + sqrt(g^2 - y^2)*t => t = c / (b-sqrt(g^2-y^2)) (5)
(2) => e = f/t + y (6)
use (5) in (6) => e = f/c * (b-sqrt(g^2-y^2)) + y

and then I let WolframAlpha solve for y (because I forgot how to do things like this myself ) which gives this:

solve e = f/c * (b-sqrt(g^2-y^2)) + y for y - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

Is this an OK solution? or is there a simpler method?

Thank you

 

[Deleted member 4993]

I have a physical problem that I already turned into a system of equations:

q*t = c + x*t (1)
e*t = f + y*t (2)
x^2 + y^2 = g^2 (3)

I wanted to solve it, but the result gets complicated and I wonder if there is a simpler solution.
I basically solve for x from (3), use that in (1) to solve for y. Then I use that in (2) to solve for t:

(3) => x = sqrt(g^2 - y^2) (4)
use (4) in (1) => q*t = c + sqrt(g^2 - y^2)*t => t = c / (b-sqrt(g^2-y^2)) (5)
(2) => e = f/t + y (6)
use (5) in (6) => e = f/c * (b-sqrt(g^2-y^2)) + y

and then I let WolframAlpha solve for y (because I forgot how to do things like this myself ) which gives this:

solve e = f/c * (b-sqrt(g^2-y^2)) + y for y - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

Is this an OK solution? or is there a simpler method?

Thank you

You have three equations - what bare your unknowns (and "knowns").

Using WA is perfectly OK with us - as long as your instructor agrees with its usage.

 

[thomasvt]

oh, sorry about that: the unknowns are x, y and t, the rest are constants...

btw, I am 38 years old gamedeveloper. Most problems I can solve myself, but i'd like some backup on this one in case I make mistakes.

thanks in advance!