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Solve systems of equations by using graphs and tables. Classify systems of equations, and determine the number of solutions. 3-1 Notes Objectives system of equations linear system consistent system inconsistent system independent system dependent system Vocabulary

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A system of equations is a set of two or more equations containing two or more variables. A linear system is a system of equations containing only linear equations.

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Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. Example 1: Verifying Solutions of Linear Systems (1, 3); x – 3y = –8 3x + 2y = 9

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Use a graph to solve the system. Check your answer. 2x – 3y = 3 y + 2 = x Example 2: Solving Linear Systems by Using Graphs and Tables

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Linear systems may also have infinitely many or no solutions. A consistent system is a set of equations or inequalities that has at least one solution. An inconsistent system will have no solutions. You can classify linear systems by comparing the slopes and y-intercepts of the equations. An independent system has equations with different slopes. A dependent system has equations with equal slopes and equal y-intercepts.

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Classify the system and determine the number of solutions. Example 3: Classifying Linear System x = 2y + 6 3x – 6y = 18

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Classify the system and determine the number of solutions. 4x + y = 1 y + 1 = –4x

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City Park Golf Course charges $20 to rent golf clubs plus $55 per hour for golf cart rental. Sea Vista Golf Course charges $35 to rent clubs plus $45 per hour to rent a cart. For what number of hours is the cost of renting clubs and a cart the same for each course?

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