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Two-Variable Equations definitions

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  • Two-Variable Equation
    Mathematical statement involving two unknowns, typically x and y, with solutions represented as ordered pairs on a coordinate plane.
  • Ordered Pair
    Combination of two numbers, usually written as (x, y), representing a point's location on a two-dimensional graph.
  • Coordinate Plane
    Two-dimensional surface defined by a horizontal x-axis and a vertical y-axis, used to plot points and graphs.
  • Solution Set
    Collection of all ordered pairs that satisfy a given two-variable equation, often forming a line or curve.
  • Graph
    Visual representation of all solutions to an equation, typically shown as a line or curve on the coordinate plane.
  • X-Intercept
    Point where a graph crosses the x-axis, always having a y-value of zero.
  • Y-Intercept
    Point where a graph crosses the y-axis, always having an x-value of zero.
  • Table of Values
    Organized chart listing selected x-values and their corresponding y-values for an equation.
  • Isolating a Variable
    Rearranging an equation so one variable, often y, stands alone on one side to simplify substitution.
  • Substitution
    Process of replacing a variable with a specific value to determine the corresponding value of another variable.
  • Number Line
    One-dimensional representation used to plot solutions of single-variable equations.
  • Axis
    Reference line on a graph; the x-axis is horizontal and the y-axis is vertical.
  • Point
    Specific location on the coordinate plane, defined by an ordered pair (x, y).
  • Infinite Solutions
    Characteristic of two-variable equations where countless ordered pairs satisfy the equation.
  • Intercepts
    Collective term for points where a graph crosses the axes, including both x-intercepts and y-intercepts.