Understanding Systems of Equations

Introduction

Systems of equations are a set of two or more equations with the same set of unknowns. Solving these systems means finding the values of the unknowns that satisfy all the equations simultaneously. 🐸 Equations can represent various real-world scenarios, and solving systems of them is key in fields such as engineering, economics, and physics.

Types of Systems

• Consistent: A system with at least one solution.
• Inconsistent: A system with no solutions.
• Dependent: A system with infinitely many solutions.

Methods of Solving

1. Graphical Method: Plotting the equations on a graph and identifying the intersection point(s).
2. Substitution Method: Solving one equation for a variable and substituting into another.
3. Elimination Method: Adding or subtracting equations to eliminate a variable.
4. Matrix Method: Using matrices and determinants to find solutions.

To practice solving systems of equations, visit our Interactive Practice Page.

Want to Learn More?

Explore more algebra topics:

• Linear Equations
• Quadratic Equations
• Polynomials