Systems of Linear Equations, Complex Numbers, and Matrices

Solving several conditions at once

Real problems often impose more than one condition simultaneously: a business balancing costs and revenues, a chemist mixing solutions to hit a target concentration, or a nutritionist blending foods to meet calorie and protein goals. A system of linear equations captures these conditions, and the solution is the set of values satisfying all of them at once. This lesson covers systems for all students; the later sections on complex numbers and matrices are HL-only extensions.

Systems of linear equations (SL and HL)

A system of two equations in two unknowns generally has one solution—the point where the lines cross.

Worked example. A cafe sells small and large coffees. On one day it sells $30$ small and $20$ large for \$190; on another, $25$ small and $30$