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Solving Systems of Linear Equations by Graphing definitions

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  • System of Equations
    A set of two or more equations with the same variables, analyzed together to find shared solutions.
  • Linear Equation
    An equation whose graph forms a straight line, typically written in the form y = mx + b.
  • Slope-Intercept Form
    A way to write equations as y = mx + b, making it easy to identify slope and y-intercept for graphing.
  • Standard Form
    An equation format written as Ax + By = C, often converted to y = mx + b for graphing.
  • Slope
    A measure of a line’s steepness, calculated as the change in y divided by the change in x.
  • Y-Intercept
    The point where a line crosses the y-axis, indicating the value of y when x is zero.
  • Intersection Point
    The coordinate where two lines cross, representing the solution to a system if it exists.
  • Parallel Lines
    Lines with identical slopes but different y-intercepts, never meeting and yielding no shared solutions.
  • Consistent System
    A system with at least one solution, meaning the equations are not contradictory.
  • Inconsistent System
    A system with no solutions, often due to parallel lines that never intersect.
  • Independent System
    A system where equations represent different lines, typically intersecting at a single point.
  • Dependent System
    A system where equations describe the same line, resulting in infinitely many solutions.
  • Solution
    A coordinate pair that satisfies all equations in a system, found at the intersection of their graphs.
  • Substitution
    A method for checking solutions by plugging values into equations to verify true statements.
  • Coordinate Pair
    An ordered pair (x, y) representing a point on the graph, used to test or express solutions.