Two-Variable Equations definitions Flashcards
Two-Variable Equations definitions
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Two-Variable Equation Mathematical statement involving two unknowns, typically x and y, whose solutions are represented as ordered pairs on a coordinate plane. Ordered Pair A set of two numbers, usually written as (x, y), representing a point's location on a two-dimensional graph. Coordinate Plane A two-dimensional surface defined by a horizontal x-axis and a vertical y-axis, used for graphing points and equations. Solution Set The collection of all ordered pairs that satisfy a given two-variable equation. Graph A visual representation of all solutions to an equation, typically shown as a line or curve on the coordinate plane. Intercept A point where a graph crosses either the x-axis or y-axis, indicating a specific value for one variable when the other is zero. X-Intercept The location on the x-axis where a graph crosses, always having a y-value of zero. Y-Intercept The location on the y-axis where a graph crosses, always having an x-value of zero. Table of Values An organized chart listing selected x-values and their corresponding y-values for a given equation. Isolating a Variable The process of rearranging an equation so that one variable, often y, stands alone on one side. Substitution The method of replacing variables in an equation with specific numerical values to check if the equation holds true. One-Variable Equation An equation involving only a single unknown, whose solution is a single value represented on a number line. Number Line A one-dimensional representation used to display solutions to equations with a single variable. Infinite Solutions A situation where an equation with two variables has countless ordered pairs that satisfy it, forming a continuous graph. Plotting Points The act of marking ordered pairs on a coordinate plane to visually represent solutions to an equation.
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