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Two Variable Systems of Linear Equations definitions

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  • System of Equations
    A set of two or more equations with the same variables that must be satisfied at the same time.
  • Linear Equation
    An equation whose graph forms a straight line, typically in the form y = mx + b or Ax + By = C.
  • Solution
    An ordered pair that makes all equations in a system true when substituted for the variables.
  • Graphical Representation
    A visual display of equations on a coordinate plane, showing where lines intersect, overlap, or run parallel.
  • Substitution Method
    A technique for solving systems by isolating a variable in one equation and replacing it in another.
  • Elimination Method
    A process of adding or subtracting equations to remove one variable, simplifying the system to a single equation.
  • Standard Form
    An arrangement of a linear equation as Ax + By = C, aligning variables and constants for easy comparison.
  • Coefficient
    A numerical factor multiplying a variable in an equation, crucial for aligning and manipulating equations.
  • Consistent Independent System
    A system with exactly one solution, represented by intersecting lines at a single point.
  • Consistent Dependent System
    A system with infinitely many solutions, represented by coincident lines overlapping completely.
  • Inconsistent System
    A system with no solution, represented by parallel lines that never intersect.
  • Intersection Point
    The coordinate pair where the graphs of two equations meet, representing the solution to the system.
  • Parallel Lines
    Lines in the same plane with equal slopes but different intercepts, never meeting and indicating no solution.
  • Coincident Lines
    Lines that lie exactly on top of each other, indicating all points are shared solutions.
  • Variable
    A symbol, often x or y, representing an unknown value in an equation or system.