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Movie Theater Ticket Sales System

Learn how to solve a system of linear equations involving ticket sales at a movie theater. Includes methods of substitution and elimination, graphing, and verifying solutions.

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Movie Theater Ticket Sales System

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  1. Section 10.1 Systems of Linear Equations; Substitution and Elimination

  2. A movie theater sells tickets for $9.00 each, with seniors receiving a discount of $2.00. One evening the theater took in $4760 in revenue. If x represents the number of tickets sold at $9.00 and y the number of tickets sold at the discounted price of $7.00, write an equation that relates these variables. Suppose that we also know that 600 tickets were sold that evening. Can you write another equation relating the variable x and y?

  3. Does a Solution Exist? • If a system has at least one solution • System is consistent • If a system has no solution, • It is called inconsistent

  4. Solving System Graphically • Solve each equation for y • Enter the first equation as y1 • Enter the second equation as y2 • Find the intersection of y1 and y2

  5. Y1 = Y2 = Solution = ( , )

  6. Verifying your answer… • Substitute your answer into the original equations and see if you get the correct number.

  7. Your turn • Is (3,3,0) a solution to

  8. Homework • Page 748 • 1,4, 6, • Solve graphically by finding the Intersection • 9,10,16,18,26,28,30,

  9. Remember…

  10. OBJECTIVE 1

  11. Procedure • Solve one of the equations for either x or y … it doesn’t matter which equation or which variable you solve for. • Select the variable with a coefficient of 1 • Substitute that solved equation into the other equation to find the other variable • Then take that value and put it into the other original equation.

  12. Your turn • Solve the system by Substitution Method (-1,5)

  13. OBJECTIVE 2

  14. Procedure Be careful of “sign” errors !!! • Multiply (or divide) each side of one of the equations by the same number (not 0) • It does not matter which equation or what you multiply by • The idea is to make one of the variables in each of the equations have the same coefficient • If possible, try to eliminate the set of variables with opposite signs. • Add (or subtract) the two equations so that one of the variables is eliminated • Solve for the variable that is left • Substitute that value into one of the original equations.

  15. Method of Elimination • Solve (2,-1)

  16. Your turn #2 • Solve the system by elimination (4,-3)

  17. A movie theater sells tickets for $9.00 each, with seniors receiving a discount of $2.00. One evening the theater sold 600 tickets and took in $4760 in revenue. How many of each type of ticket were sold?

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