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Solving Systems of Linear Equations by Graphing definitions

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  • System of Equations
    A collection of two or more equations requiring a single set of values to satisfy all simultaneously.
  • Linear Equation
    An equation whose graph forms a straight line, typically written in slope-intercept or standard form.
  • Slope-Intercept Form
    A format for expressing equations as y = mx + b, highlighting both slope and y-intercept.
  • Standard Form
    An arrangement of equations as Ax + By = C, often requiring conversion for graphing.
  • Intersection Point
    The coordinate where two lines cross, representing the solution to a system.
  • Slope
    A measure of a line’s steepness, indicating the rate of change between x and y.
  • Y-Intercept
    The location where a line crosses the y-axis, revealing the value of y when x is zero.
  • Parallel Lines
    Lines with identical slopes but different y-intercepts, never meeting and yielding no solution.
  • Consistent System
    A system with at least one solution, where lines intersect or overlap.
  • Inconsistent System
    A system with no solution, typically represented by parallel lines.
  • Independent System
    A system where lines intersect at a single point, each line distinct.
  • Dependent System
    A system where lines coincide, resulting in infinitely many solutions.
  • Solution Set
    All coordinate pairs that satisfy every equation in a system.
  • Graphing
    A visual method for representing equations and identifying intersection points.
  • Coordinate Pair
    An ordered pair (x, y) representing a point on the graph.