Unique Solutions in Linear Equations
In this section, we explore the characteristics of linear equations with two variables, emphasizing that unlike linear equations in one variable, which have a unique solution, linear equations in two variables can have infinitely many solutions. A solution to such an equation is represented as an ordered pair (x, y) that satisfies the equation. For example, the equation 2x + 3y = 12
has solutions such as (3, 2), (0, 4), and even (6, 0). This is because by choosing different values for either variable, corresponding values can be calculated for the other variable.
Further, the section illustrates finding solutions through various approaches, including substituting values directly and validating whether given pairs are indeed solutions to the equations. A focus is laid on practical exercises and examples demonstrating how a single equation can yield multiple valid solutions, reflecting the richness and flexibility in handling two-variable linear equations.