Mastering Mathematics Smartly
by Wee Wen Shih

A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.

System of linear equations

This 6-page document highlights the essentials for this topic.

Note: It is already possible for students using TI graphic calculators to use the application called PlySmlt2 to solve a system of linear equations. Follow these steps:
1. In the main menu upon entering the application, select option 2 (SIMULT EQN SOLVER).

2. Then specifiy the values for EQUATIONS and UNKNOWNS. Press NEXT.

3. Enter the values for the rows and columns of the matrix. Press SOLVE.

Geometric interpretations

(1) Equations in two variables:

  • One unique solution: This means that the 2 lines intersect at a point.
  • No solution: This means that the 2 lines do not intersect at all. They are parallel.
  • Infinitely many solutions: This means that the 2 lines coincide with each other.

(2) Equations in three variables (visualise):

  • One unique solution: This means that the 3 planes intersect at a point.
  • No solution: This means that the 3 planes do not have a point in common.
  • Infinitely many solutions: This means that the 3 lines intersect in one line.