Lesson 22 ~ Parallel, Intersecting or the Same Line

Transcription

1 Lesson ~ Parallel, Intersecting or the Same Line Graph the two linear equations in each system on a single coordinate plane and state whether the lines are intersecting, parallel or the same line.. x 5 x +. 4 x x y = 6 x + Determine if the two lines are intersecting, parallel or the same lines by comparing the linear equations in slope-intercept form. State how many solutions there will be for each system. x + x y = 6x ( x 6) ( x + ) x = 8 = 9. 4x 5 8x +. Two airplanes mapped their courses on a coordinate grid. The first plane followed a path of 8. The second airplane flew its daily flight on the path 6x + y = 6. Describe the similarities or differences in the planes paths. 8 SM C Curriculum Oregon Focus on Linear Equations

2 Lesson ~ Solving Systems by Graphing Decide whether the given ordered pair is a solution to the system of equations.. x 6. x + 5y = 8. 5 x + x + 8 7x 4 x (4, ) (, ) (, ) Solve each system of equations by graphing. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. x + 5. x 5 6. ( x + ) x + 6 = x + y SOLUTION: SOLUTION: SOLUTION: 7. x 8. x x + y = 9 x 5 x + 4 x + SOLUTION: SOLUTION: SOLUTION: 8 SM C Curriculum Oregon Focus on Linear Equations

3 Lesson 4 ~ Solving Systems Using Tables Solve each system of equations using the given input-output tables.. 4x x + 5. x + x x y x y x y x y x + 6 x x x y x y x y x y x 6. x + 5( x + ) x y x y x y x y 7. Mikayla put $ in a savings account at the beginning of the year. At the end of each month, she withdrew $ from her account. Matthew put $ in his savings account at the beginning of the year. At the end of each month, he deposited $4 in his account. Let x represent the number of months which have passed and y represent the amount in each savings account. a. Write an equation to represent the amount in Mikayla s savings account. b. Write an equation to represent the amount in Matthew s savings account. c. On the back of this worksheet, make input-output tables that show the amount in each account for the first 8 months. d. When will Mikayla and Matthew have the same amount in their accounts? 8 SM C Curriculum Oregon Focus on Linear Equations

4 Lesson 5 ~ Solving Systems By Substitution Solve the system of equations using the substitution method. Check the solution.. x +. x + 6 x + y = x = y. 6 x + 5y = 6 4x y = 5 x = 5 y x x = y 6. y + x = 7 x + y = y x = 9 7. Reese picked two numbers, x and y. She told her friend that the sum of the two numbers is 9 and the difference of the two numbers is 7. a. Write two different linear equations that model what Reese told her friend. b. Solve the system of linear equations using the substitution method. What two numbers did Reese pick? 8 SM C Curriculum Oregon Focus on Linear Equations

5 Lesson 6 ~ Solving Systems Using Elimination Solve each system of equations using the elimination method. Check the solution. y =.. 7x + y = x + 5y = 9 x + y = y = y = x 6y = 54 4x + y = 4 6 = 4x + y = 4x y 4x x y = 4x y = 8. x 4y = 4x + y = 8 SM C Curriculum Oregon Focus on Linear Equations

6 Lesson 7 ~ Choosing the Best Method Choose the best method to solve each system of linear equations and explain your reasoning.. x Method: 4 + Reason:. 4 x 5y = 9 Method: 6x Reason:. x + y = 8 Method: x y = 8 Reason: State the best method to solve each system of linear equations and then solve. x + x + 4y = 8 5. x x x x + 6x 8 SM C Curriculum Oregon Focus on Linear Equations

7 Lesson 8 ~ Applications of Systems of Equations Define the variables and develop a system of equations for each problem. Solve the system and check your solution. Write your answer in a complete sentence.. Two bike rental companies have different pricing systems. Company A charges a flat fee of $4 plus $ per hour. Company B does not charge a flat fee but charges $.8 per mile driven. At what distance do both companies charge the same amount?. Two teachers, Mr. Meehan and Mrs. Chipps, decide to buy compasses and rulers for their classrooms. Mrs. Chipps buys compasses and 5 rulers for $95. Mr. Meehan buys 4 of each for $6. What are the individual costs of the compasses and rulers that were purchased?. Lesley bought 4 bags of pretzels and boxes of granola bars for $.5. Landon bought bag of pretzels and 5 boxes of granola bars for $7.55. What is the cost for one bag of pretzels? What is the cost for a box of granola bars? SaveLots offers two types of baseball bats. The wood bats sell for $4 and the metal bats sell for $. In one day, SaveLots sold baseball bats. The receipts for those bats totaled $66. How many of each type of bat were sold? 8 SM C Curriculum Oregon Focus on Linear Equations