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, requiring solutions that satisfy all equations simultaneously. Linear Equation An equation whose graph forms a straight line, typically involving variables raised only to the first power. Solution An ordered pair that makes all equations in a system true when substituted for the variables. Graphing Method A technique for solving systems by plotting equations and identifying intersection points as solutions. Substitution Method A process where one variable is isolated in an equation and its expression is substituted into another equation. Elimination Method A strategy involving adding or subtracting equations to remove one variable, often after adjusting coefficients. Standard Form An arrangement of a linear equation as Ax + By = C, aligning variables and constants for systematic solving. Coefficient A numerical factor multiplying a variable in an equation, crucial for aligning terms in elimination. 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, where all equations represent the same line. Inconsistent System A system with no solution, typically shown by parallel lines that never intersect. Intersection Point The coordinate where the graphs of equations in a system cross, representing the solution. Parallel Lines Graphs of equations with identical slopes but different intercepts, indicating no shared solution. True Statement A result from substituting values into equations where both sides are equal, confirming a solution. False Statement A result from substituting values into equations where both sides are unequal, indicating no solution.
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