1Cademy - Solution of a Linear Equation in Two Variables

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Solution of a Linear Equation in Two Variables

An ordered pair (x, y) is a solution to a linear equation in two variables, such as $Ax + By = C$ , if substituting the $x$ - and $y$ -values into the equation results in a mathematically true statement. Here $A$ , $B$ , and $C$ are real numbers, with $A$ and $B$ not both zero. If $B\ne0$ , each real $x$ gives exactly one corresponding value $y=(C-Ax)/B$ . If $B=0$ , then $A\ne0$ and $x=C/A$ is fixed, while any real $y$ is allowed. Both cases yield infinitely many real solutions. For example, $x=2$ , equivalently $1x+0y=2$ , has solutions (2,y) for every real $y$ ; however, $x=0$ gives $0=2$ regardless of $y$ , so no corresponding $y$ exists.

Updated 2026-10-07

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