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Math Help - eliminate parameters, multivaraible

  1. #1
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    eliminate parameters, multivaraible

    question: a plane is given by the equation \pi=x=60s+2t,y=s+t,z=s+3t eliminate s and t and put the equation into the form ax+by+cz=d.
    work: s=\frac{2(y+3)-x}{3} and t=\frac{x+y-6}{3} Plug them into original x,y,z equations and solve for x,y,z
    problem: I don't know how to combine 3 equations into 1
    Last edited by superdude; October 27th 2009 at 10:24 PM. Reason: changed work
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  2. #2
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    Quote Originally Posted by superdude View Post
    question: a plane is given by the equation \pi=x=60s+2t,y=s+t,z=s+3t eliminate s and t and put the equation into the form ax+by+cz=d.
    work: s=\frac{2(y+3)-x}{3} and t=\frac{x+y-6}{3} Plug them into original x,y,z equations and solve for x,y,z
    problem: I don't know how to combine 3 equations into 1
    Just substitute your expressions for s and t into z = s + 3t.

    Personally, this is how I'd solve the question:
    Solve y = s + t and z = s + 3t simultaneously to get s and t in terms of y and z. Now substitute these solutions for s and t into x = 60s + 2t.
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