Week 1: Systems of Linear Equations

LINEAR SYSTEMS

What is a Linear Equation?

A linear equation describes a straight line (in 2D) or a plane (in 3D).

A linear equation in $n$ variables $x_1, x_2, \dots, x_n$ is an equation of the form:

$a_1x_1 + a_2x_2 + \dots + a_nx_n = b$

Key Concept

A system of linear equations is a collection of one or more linear equations involving the same variables.

✨ Example System

\begin{cases} 2x + 3y = 5 \\ 4x - y = 3 \end{cases}