Each graph below is the graph of a system of three linear eq

Each graph below is the graph of a system of three linear equations in three unknowns of the form Ax = b. Determine whether each system has a solution and, if it does, the number of free variables.

Solution

A)  There is no solution. The three planes do not have any points in common.

B) There is one solution. In order for three equations with three variables to have one solution intersect at single point

C) Again: The three planes do not have any points in common- No solution

D) That two of the equations may have points in common with each other, but not all three- No solution

E) Yes one solution: three equations with three variables to have one solution, the planes must intersect in a single point.