How can I re-write an equation (or system of equations) in parametric form?

Question

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 $t$?

@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

score 5 · Accepted Answer · answered Nov 10 '12 at 21:37

5

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 $y=3t$.

answered Nov 10 '12 at 21:37

Mike D.

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
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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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