Notebook Quiz #2: Complete on a separate sheet of paper.

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Presentation transcript:

Notebook Quiz #2: Complete on a separate sheet of paper. 1. Another method for solving systems of equations is elimination. 2. Like substitution, the goal of elimination is to get one equation that has only one variable. 3. To do this by elimination, you add the two equations in the system together. Solve the systems using elimination: 4. 2𝑥+𝑦=3 −𝑥+3𝑦=−12 5. −5𝑥+2𝑦=32 2𝑥+3𝑦=10 3, −3 −4, 6

Objective: Today we will apply systems of equations to real world problems.

Example 1: What information do we know? The school that Kristin goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 13 senior citizen tickets and 14 student tickets for a total of $219. The school took in $41 on the second day by selling 6 senior citizen tickets and 1 student ticket. Find the price of a senior citizen ticket and the price of a student ticket. What information do we know? Let 𝑥= the price of senior citizen ticket Let 𝑦= the price of a student ticket The first equation will represent the total number of tickets sold on day one: 13 Senior citizen tickets + 14student tickets = total amount 13𝑥+14𝑦=219 The second equation will represent the total number of tickets sold on day two: 6𝑥+1𝑦=41

Example 1 continued… Write your system of equations: 13𝑥+14𝑦=219 6𝑥+𝑦=41 Solve the system using substitution: Solve the second equation for 𝑦 by subtracting 6𝑥 on both sides: 6𝑥+𝑦=41 −6𝑥 −6𝑥 𝑦=−6𝑥+41 Substitute the value of 𝑦 into the first equation: 13𝑥+14𝑦=219 13𝑥+14 −6𝑥+41 =219

Example 1 continued… Solve the equation for 𝑥: 13𝑥+14 −6𝑥+41 =219 13𝑥−84𝑥+574=219 −71𝑥+574=219 −574 −574 −71𝑥=−355 −71 −71 𝑥=5 Substitute the value of 𝑥 into the second equation and solve for 𝑦: 6𝑥+𝑦=41 6 5 +𝑦=41 30+𝑦=41 −30 −30 𝑦=11

Example 1 continued… Write the answers to the problem: Since 𝑥= the price of a senior citizen ticket, a senior citizen ticket costs $5. Since 𝑦= the price of a student ticket, a student ticket costs $11.

Example 2: The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 13 vans and 6 buses with 368 students. High School B rented and filled 2 vans and 12 buses with 544 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Example 3: Matt and Shawna are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and apple cheesecakes. Matt sold 7 pecan cheesecakes and 2 apple cheesecakes for a total of $75. Shawna sold 1 pecan cheesecake and 14 apple cheesecakes for a total of $285. Find the cost each of one pecan cheesecake and one apple cheesecake.