Need explanation of multivariable calculus question

Question

Give a geometric description of the set of points in space whose coordinates satisfy the pair of equations

i) x = 2 ,y = 3

ii) x=-1,z=0

iii)y=0,z=0

iv)x=1,y=0

Answer 1

All of these are lines. If you specify two coordinates, you have limited the function to a point in that plane. If the third coordinate is unspecified, it can have any value, which leads to a line parallel to that coordinate axis and perpendicular to the plane of the first two coordinates.

i) A line parallel to the z axis going through the point (x,y) = (2,3) In 3d you can think of the function as

(2,3, z)

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