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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 whose solutions are coordinate pairs that satisfy all equations simultaneously.
  • Linear Equation
    An equation whose graph forms a straight line, often written in slope-intercept or standard form.
  • Slope-Intercept Form
    An equation format y = mx + b, where m is the slope and b is the y-intercept, making graphing straightforward.
  • Standard Form
    An equation format like Ax + By = C, which can be rearranged to slope-intercept form for easier graphing.
  • Slope
    A value indicating the steepness and direction of a line, found in the coefficient of x in y = mx + b.
  • Y-Intercept
    The point where a line crosses the y-axis, represented by the constant b in y = mx + b.
  • Intersection Point
    The coordinate pair where two lines cross, representing the solution to a system of equations.
  • Parallel Lines
    Lines with identical slopes but different y-intercepts, never crossing and yielding no solution.
  • Consistent System
    A system with at least one solution, either a single intersection or overlapping lines.
  • Independent System
    A system where lines intersect at a single point, indicating only one solution.
  • Dependent System
    A system where lines overlap completely, resulting in infinitely many solutions.
  • Inconsistent System
    A system with no solution, typically due to parallel lines that never intersect.
  • Coordinate Pair
    An ordered pair (x, y) representing a point on the graph that may satisfy one or more equations.
  • True Statement
    An equation outcome where substituted values make both sides equal, confirming a solution.
  • Polynomial Term
    A part of an algebraic expression, such as 3x or -4, often used in forming equations.