'Intersection of Two Planes' lesson under vectors. Please help. I have attached the answer as well. I want to know how they concluded with those answers.

QUESTION 1:

a. -' m A system of two equations in three unknowns has been manipulated, and, after correctly using elementary operations, a student arrives at the following equivalent system of equations: xy+z=1 x+y+z=3 1ln'll'hat does this equivalent system mean? A system of two equations in three unknowns has been manipulated, and, after correctly using elementary operations, a student arrives at the following equivalent system of equations: 2xy+22=1 x+y+z= 1F.I"1.I']1at does this equivalent system mean? A system of two equations in three unknowns has been manipulated, and, after correctly using elementary operations, a student arrives at the following equivalent system of equations: xy+z=1 x+y+22=4 1ln'll'hat does this equivalent system mean? 1. a. The two equations represent planes that are parallel and not coincident. b. Answers may vary. For example: x-y+z=l,x-y+z=-2 2. a. X= + s - Ly = S, Z = 1; 2 s, fER; the two planes are coincident. b. Answers may vary. For example: x-ytz=-1, 2x - 2y + 2z = -2 3. a. x = 1 + s,y = s,z= -2, sER; the two planes intersect in a line.Determine the vector equation of the line that passes through the point A(-2,3,6) and is parallel to the line of intersection between the two planes n,: 2x - y + z = 0 and 12: y + 4z = 0.