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.

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.

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