# eliminate parameters, multivaraible

• Oct 27th 2009, 10:16 PM
superdude
eliminate parameters, multivaraible
question: a plane is given by the equation $\displaystyle \pi=x=60s+2t,y=s+t,z=s+3t$ eliminate s and t and put the equation into the form ax+by+cz=d.
work: $\displaystyle s=\frac{2(y+3)-x}{3}$ and $\displaystyle t=\frac{x+y-6}{3}$ 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
• Oct 28th 2009, 12:10 AM
mr fantastic
Quote:

Originally Posted by superdude
question: a plane is given by the equation $\displaystyle \pi=x=60s+2t,y=s+t,z=s+3t$ eliminate s and t and put the equation into the form ax+by+cz=d.
work: $\displaystyle s=\frac{2(y+3)-x}{3}$ and $\displaystyle t=\frac{x+y-6}{3}$ 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.