Two Variable Systems of Linear Equations definitions Flashcards
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.
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