Introduction to Systems of Linear Equations

This chapter presents the definition and notation of systems of linear equations. The point of intersection of the two lines is a key point of interest when considering a system of equations. The chapter provides the solution to a system of two linear equations in two variables. A proposed solution to a system of linear equations can be checked by ensuring the coordinates satisfy all the equations of the system. A system of linear equations can be classified as consistent, inconsistent, or dependent. There are situations that arise in many areas of mathematics and science whose nature leads to a system of equations. Matrices are a fundamental tool in linear algebra and are used to represent and manipulate systems of linear equations. The chapter introduces the concept of matrices and explores various properties related to matrix invertibility. It focuses on using matrices to solve systems of linear equations.