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Exploration of pair of linear equations in two variables offers insights into graphical and algebraic methods for finding solutions. Key concepts include identifying consistent, inconsistent, and dependent systems of equations while analyzing their graphical representations. Various mathematical representations and methods to approach these equations are emphasized throughout the chapter.
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Term: Consistent Pair of Linear Equations
Definition: A pair of linear equations that has at least one solution. Graphically, represented by two intersecting lines.
Term: Inconsistent Pair of Linear Equations
Definition: A pair of linear equations that do not have any solutions, represented by parallel lines.
Term: Dependent Pair of Linear Equations
Definition: A pair of linear equations that has infinitely many solutions, represented by coincident lines.
Term: Graphical Method
Definition: A method of solving linear equations by plotting their graphs and identifying points of intersection.
Term: Algebraic Methods
Definition: Techniques like substitution and elimination used to solve pairs of linear equations by manipulating the equations algebraically.