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Practice ExercisesPractice Exercises► Perform the indicated operationPerform the indicated operation
► Graph each pair of linear equation on the same set of axes. Graph each pair of linear equation on the same set of axes.
3x – y = - 22x + 2y = -12
y = - ½ x +3y = - ½ x – 1
y + x = 34y + 4x = 12
System of Linear System of Linear EquationEquation
Graphical Graphical SolutionSolution
Types of System of Types of System of Linear Equation in Linear Equation in
Two VariablesTwo Variables
► Independent SystemIndependent System Graph: Intersecting LinesGraph: Intersecting Lines Solution: One SolutionSolution: One Solution
► Inconsistent SystemInconsistent System Graph: Parallel LinesGraph: Parallel Lines Solution: No SolutionSolution: No Solution
►Dependent SystemDependent System Graph: Coincident LinesGraph: Coincident Lines Solution: Infinite number of SolutionSolution: Infinite number of Solution
Activity: Cooperative LearningActivity: Cooperative Learning► Graph the following system, then Graph the following system, then
determine whether the system is determine whether the system is independentindependent, , inconsistentinconsistent, or , or dependentdependent
x + y = 2 x – y = - 1a.
x + 2y = 42x + 4y = 8
b.
y = 3x + 5 y – 3x = - 6 c.
d. 2x + y = 36x + 3y = 9
► Another way to determine Another way to determine whether the system is whether the system is INDEPENDENTINDEPENDENT, , INCONSISTENTINCONSISTENT, or , or DEPENDENTDEPENDENT is by comparing is by comparing the the SLOPESSLOPES and the and the Y–Y–INTERCEPTINTERCEPT of the system of the of the system of the form form y= mx + by= mx + b