Detailed Summary
In this section, we explored the definition and representation of linear equations in two variables. A linear equation can generally be expressed in the form:
$$ ax + by + c = 0 $$
where a, b, and c are real numbers, and both a and b cannot be zero simultaneously. Each equation corresponds to a geometric representation on a Cartesian plane, where every point (x, y) that lies on the line defined by the equation represents a solution.
The section also covered how to express different forms of equations in this standard linear form, illustrated by several examples. Additionally, it discussed the infinite number of solutions such equations possess, emphasizing that any point on the line is a solution, and methods to identify specific solutions through substitution were provided.
This exploration lays the foundation for understanding the graphical representation of linear equations and their real-world applications.