How can I convert three parametric equations into a system of two equations with 3 unknowns?

Mathematics
Tutor: None Selected Time limit: 1 Day

I have the set of parametric equations x=1-2t, y=4+3t and z=-1+t. I need to figure out how to find a system of two equations that will have that solution. This is for a linear algebra class.

Oct 20th, 2015

Hello!

Let's express these equation in the form t=something:

x=1-2t, t = (1-x)/2,
y=4+3t, t = (y-4)/3,
z=-1+t, t = z+1.

t=t, therefore

(1-x)/2 = z+1,
(y-4)/3 = z+1.
(we may choose any two pairs), or with integer coefficients

x+2z+1=0,
y-3z-7=0.

The third possible equation, (1-x)/2 = (y-4)/3, is dependent from the first two.

Please ask if something is unclear.
Oct 20th, 2015

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