Problem-4

Question

Give a geometric representation of a system of three equations in three unknowns that has a unique solution.

Solution

Each equation in three variables represents a plane in \(\mathbb{R}^{3}\). There is a unique solution if the three planes intersect at a point. Any two non-parallel planes intersect in a line. The third plane intersects this line at exactly one point. The red point in the image below is the intersection point of three planes.