---
title: Systems of Equations
description: Systems of equations are collections of two or more equations sharing common variables. Learners will understand how to find simultaneous solutions using substitution, elimination, and matrix methods, allowing them to model complex scenarios with multiple constraints.
category: mathematics
subcategory: algebra
difficulty: beginner, intermediate, advanced
url: /subject/systems-of-equations
---

# Systems of Equations

Systems of equations are collections of two or more equations sharing common variables. Learners will understand how to find simultaneous solutions using substitution, elimination, and matrix methods, allowing them to model complex scenarios with multiple constraints.

## Available Resources

3 Courses • 4 Websites

## Websites

### 1. MathIsFun

Illustrated introductory page on systems of linear equations, solving two- and three-variable systems by substitution and elimination with step-by-step worked examples. Readers learn why a system has one solution, no solution or infinitely many, and what consistent and inconsistent mean.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.mathsisfun.com/algebra/systems-linear-equations.html

**Tags:** systems-of-equations, linear-equations, algebra, substitution-method, elimination-method

### 2. Purplemath

Seven-page Purplemath module on linear systems: definitions, graphing, special cases, substitution, elimination, and Gaussian elimination, with worked examples. Learners can classify systems as consistent, inconsistent, or dependent and solve them by hand.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.purplemath.com/modules/systlin1.htm

**Tags:** systems-of-equations, linear-equations, substitution-method, elimination-method, algebra

### 3. Khan Academy

Interactive lessons and practice problems on systems of equations

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-with-substitution

### 4. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Courses

### 1. Systems of Equations and Inequalities

Master solving systems of equations and inequalities with this comprehensive course from Khan Academy. Learn algebraic techniques and graphical solutions!

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra-home/alg-system-of-equations

**Tags:** systems-of-equations, systems-of-inequalities, linear-equations, substitution-method, elimination-method, algebra-1

### 2. Linear Algebra - Foundations to Frontiers

Learn the mathematics behind linear algebra and link it to matrix software development.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://www.edx.org/learn/linear-algebra/the-university-of-texas-at-austin-linear-algebra-foundations-to-frontiers

**Tags:** courses, mathematics-statistics, linear-algebra

### 3. Algebra: Elementary to Advanced - Polynomials and Roots

**Author:** Joseph W. Cutrone

Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/polynomials-roots

**Tags:** polynomials, factoring, exponents, radicals, algebra

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