Slide 1 :
Lesson 5 Menu : Lesson 5 Menu Five-Minute Check (over Lesson 5-4)
Main Ideas
California Standards
Key Concept: Solving Systems of Equations
Example 1: Determine the Best Method
Example 2: Real-World Example
Lesson 5 MI/Vocab : Lesson 5 MI/Vocab Determine the best method for solving systems of equations. Apply systems of linear equations.
Lesson 5 CA : Lesson 5 CA Standard 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Key, CAHSEE)
Key Concept 5-5a : Key Concept 5-5a
Lesson 5 Ex1 : Lesson 5 Ex1 FUND-RAISING At a Boy Scout fund-raising dinner, Mr. Jones bought 2 adult meals and 3 child meals for $23. Mrs. Gomez bought 4 adult meals and 2 child meals for $34. All adult meals are the same price and all child meals are the same price. The following system can be used to represent this situation. Determine the best method to solve the system of equations. Then solve the system.
2x + 3y = 234x + 2y = 34 For an exact solution, an algebraic method is best.
Since neither the coefficients of x nor the coefficients of y are 1 or –1, you cannot use the substitution method. Determine the Best Method
Lesson 5 Ex1 : Lesson 5 Ex1 Since the coefficients are not the same for either x or y, you will need to use elimination with multiplication. Multiply the first equation by –2 so the coefficients of the x-terms are additive inverses. Then add the equations. Determine the Best Method 2x + 3y = 23
4x + 2y = 34 –4y = –12 Add the equations. Divide each side by –4. y = 3 Simplify.
Lesson 5 Ex1 : Lesson 5 Ex1 Now substitute 3 for y in either equation to find the value of x. Answer: The solution is (7, 3). So, adult meals cost $7 and child meals cost $3. Determine the Best Method 4x + 2y = 34 Second equation
4x + 2(3) = 34 y = 3
4x + 6 = 34 Simplify.
4x + 6 – 6 = 34 – 6 Subtract 6 from each side.
4x = 28 Simplify. Divide each side by 4. x = 7 Simplify.
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B
C
D A. (4, 3) B. (4, 4)
C. (3, 3) D. (–4, –3) POOL PARTY At the school pool party, Mr. Lewis bought 1 adult ticket and 2 child tickets for $10. Mrs. Vroom bought 2 adult tickets and 3 child tickets for $17. All adult tickets are the same price and all child tickets are the same price. The following system can be used to represent this situation. Determine the best method to solve the system of equations. Then solve the system.x + 2y = 102x + 3y = 17
Lesson 5 Ex2 : Lesson 5 Ex2 CAR RENTAL Ace Car Rental rents a car for $45 a day and $0.25 per mile. Star Car Rental rents a car for $35 per day and $0.30 per mile. How many miles would a driver need to drive before the cost of renting a car at Ace Car Rental and renting a car at Star Car Rental were the same? Explore You know the cost to rent a car for each company.
Plan Write an equation to represent the cost for each company. Then solve.
Solve Let x = the number of miles and y = the cost of renting a car.
Ace Car Rental: y = 45 + 0.25xStar Car Rental: y = 35 + 0.30x
Lesson 5 Ex2 : Lesson 5 Ex2 You can use elimination to solve. Answer: This means that after 200 miles, the cost will be the same. Check Check by sketching a graph of the equations. The graphs appear to intersect at (200, 95) which verifies that x = 200. 0 = 10 – 0.05x
–10 = –0.05x
200 = x
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B
C
D A. 8 days
B. 4 days
C. 2 days
D. 1 day VIDEO GAMES The cost to rent a video game from Action Video is $2 plus $0.50 per day. The cost to rent a video game at TeeVee Rentals is $1 plus $0.75 per day. After how many days will the cost of renting a video game at Action Video be the same as the cost of renting a video game at TeeVee Rentals?
End of Lesson 5 : End of Lesson 5