3D Intersection Visualizer

Algebra 2 · Axiom Academy

Every equation in x, y, and z is a flat plane in space. Where the planes cross is the solution — and that meeting can be a single point, a whole line, or nowhere at all. A single equation like x + y = 3 doesn't pin down one answer in 3D — a whole flat plane of points satisfies it. So how does a system of three such equations ever land on one solution? Watch what happens as the planes stack up. Each new plane is one more equation, and each one narrows where the answer can live. Three planes together can trap the solution down to a single point. Two planes meet along a line; the third plane slices that line down to one point — the unique triple that solves all three equations at once. Three planes, three kinds of answer Keep the first two equations fixed — their planes cross along one line. Now switch the third equation and drag the figure to rotate it. How the third plane sits against that line is the whole story. The third plane cuts straight across the line where the first two meet, pinning the answer to one point: (1, 2, 2) . Cross the line, and you get one point. Lie along it, and every point on the line works. Run parallel but miss it, and the three planes never share a point at all. Geometry first, algebra second

This is the written version of the interactive lesson above. See the full Algebra 2 course.