Understanding Linear Equations

Core concept

For example, the equation 2x+3y=6 is satisfied by infinitely many ordered pairs, including (0,2), (3,0), and (1.5,1) — each can be verified by substitution. This concept of multiple solutions to a single equation is a key difference from equations in one variable, and understanding it prepares students for studying pairs of simultaneous equations, where finding a solution that satisfies TWO equations at once narrows down the infinite possibilities to typically just one unique solution.