\"write a system of three equations in three unknowns for which the the solution

Question

"write a system of three equations in three unknowns for which the the solutions form a single plane in R3. Determine the parametric equation of the plane" (problem 3.2 #10  from Diff Equations & Linear Algebra Farlow Hall 2nd Ed.)

I am confused on how to approach this problem, and the Chegg solution confused me more. Unless the equations were multiples of each other i.e the "same plane" how could these planes exist at anything more than a single vector, single point, or parallel lines ?  

The Chegg solution as follows

for the system of equations;

3x+2y-z=1

2x-2y+4z=-2

-x+.5y-z=0

the solution given as

x-2y-2z=0

When I graph these equations I cannot see how the plane x-2y-2z=0 is a solution for the other 3.

Explanation / Answer

I think there is something missing in the question because the three equations written are themselves equation of planes and thus a common solution to all three of them would only be a point.

(Intersection of two non-parallel planes give a line and intersection of 3 non parallel planes gives a point.)

However the solution mentioned is an equation of a plane.

Feel free to ask any other query.

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