In this section, linear equations in two variables are defined as equations that can be expressed in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. The section starts by recalling previous knowledge of linear equations in one variable and extends it to two variables, focusing on questions such as whether solutions exist and their uniqueness.
Examples demonstrate how to convert various equations into the standard form and identify their coefficients. The section highlights that a linear equation in two variables has infinitely many solutions, where each solution corresponds to a point on the Cartesian plane. Additionally, exercises encourage students to practice identifying and writing linear equations, while examples illustrate the method of finding solutions by setting values for one variable and solving for the other. Overall, this section lays the foundation for understanding linear equations and their representation, preparing students for further exploration in the chapter.