This section provides step-by-step examples for solving systems of linear equations. You will learn how to apply the Substitution and Elimination methods to find the intersection points of lines in 2D and planes in 3D.

A system of linear equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines). Here are case studies demonstrating these types.

The Substitution method works well when one variable is easily isolated. The Elimination method is generally faster when both equations are in standard form ($Ax + By = C$).

Solving a system with three variables ($x, y, z$) requires eliminating one variable at a time using pairs of equations, reducing the problem to a two-variable system.