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For the equation $y = 3x$ I need to re-write $x$ and $y$ in terms of a variable $t$. How can I find the value of each variable in terms of $t$?

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Have you tried something simple like letting $x=t$? – chris Nov 10 '12 at 21:35
@chris Yes, that would work (at least in this case). – Anderson Green Nov 10 '12 at 21:35
@chris In general, is it possible to re-write an equation in parametric form by letting one of the variables equal t, and then writing each variable in terms of that variable? (This seems like the most obvious solution to me, but I could be mistaken.) – Anderson Green Nov 10 '12 at 21:37
up vote 5 down vote accepted

If $y=f(x)$ is a function of $x$ we can write parametric equations by writing $x=t$ and $y=f(t)$. So in your example we write $x=t$ and $y=3t$.

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Could you apply the same method to the system of equations x = 2y, z = 3y, q = 2z? (then y = t/2, z = 3t/2, q = 3t)? – Anderson Green Nov 10 '12 at 21:42
Affirmative, and your solution y = t/2, z = 3t/2, q = 3t looks good. – Mike D. Nov 10 '12 at 21:48

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