# Solving Systems of Linear Equations Putting it All Together

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2 Step 3 Using the handout Solving Systems of Equations: Which Strategy Works Best? Solving the System Part 2, students will solve each system using their selected strategy. Work individually or in pairs; then share answers with the class. Step 4 Students will take the Writing & Solving Systems of Equations Quiz to evaluate the unit on Solving Systems of Linear Equations. Assessment/Evidence (based on outcome) Teacher observation of students choices Completed Venn diagram or chart Completion of Writing & Solving Systems of Equations handout Teacher Reflection/Lesson Evaluation This lesson has not yet been field tested. Next Steps An excellent way to extend or give students more practice with systems of equations is to follow up with a lesson determining the best cell phone plan to purchase. Here are a couple places to find these lessons online: Cell Phone Plans or Purchase a Cell Phone with Systems of Equations Technology Integration Venn Diagram Teaching Strategy Virtual Math Lab: Intermediate Algebra Yay Math Purposeful/Transparent Transitions classes focus on higher level math skills, such as solving systems of equations that will be required for college classes. Contextual Students will determine the best method to use when solving systems of equations as they solve problems using graphing, substitution, and /addition. Building Expertise Students are given amble practice working in graphing, substitution, and /addition of linear equations and write a system of equations when solving a mathematical situation.

3 Solving Systems of Equations - Which Strategy Works Best? Solution Strategies Part 1 Directions Cut out the problems found below. Decide which strategy (graphing, substitution, or ) is the best to solve each system. Tape or glue the system in the column under the strategy you selected. Be prepared to explain why you selected that strategy to solve the solution, including the characteristics of the system. Graphing Substitution Elimination Cut the problems below to put on chart above x y = 8 x + y = 4 5a b = -9 4a + 3b = -11 7a + 6b = 0 15a 6b = 0 2w 3q = 8 3w 7q = t + 3n = 9 5t 3n = 5 2r + s = 11 r s = 2 y = 3x 1 y = 2x x 5y = 7 3x 2y = -17 y = 3 x 5x + 3y = -1 2y = 8 7x 4y = 16 14x

4 Solving Systems of Equations - Which Strategy Works Best? Solving the System Part 2 Directions Solve each system using the strategy you selected in Solution Strategies Part 1 of this activity. Show your work and the solution in each box below. 1 2x y = 8 x + y = 4 2 2t + 3n = 9 5t 3n = 5 3 2x 5y = 7 3x 2y = a b = -9 4a + 3b = r + s = 11 r s = 2 6 y = 3 x 5x + 3y = a + 6b = 0 15a 6b = 0 8 y = 3x 1 y = 2x 5 9 2y = 8 7x 4y = 16 14x 10 2w 3q = 8 3w 7q = 7

5 Solving Systems of Equations - Which Strategy Works Best? ANSWER KEY Parts 1 & 2 problem answers possible strategy 1 2x y = 8 x + y = 4 x = 4 y = 0 substitution 2 2t + 3n = 9 t = 2 5t 3n = 5 n = 5/3 3 2x 5y = 7 y = -5 3x 2y = -17 x = a b = -9 4a + 3b = -11 a = -2 b = -1 substitution 5 2r + s = 11 r s = 2 r = 4 ⅓ s = 2 ⅓ substitution 6 y = 3 x x = -5 substitution 5x + 3y = -1 y = 8 7 7a + 6b = 0 a = 0 15a 6b = 0 b = 0 8 y = 3x 1 y = 2x 5 x = -4 y = -13 graphing substitution 9 2y = 8 7x 4y = 16 14x no solution graphing 10 2w 3q = 8 3w 7q = 7 q = 2 w = 7

6 Solving Systems of Linear Equations Venn Diagram Graphing Substitution Elimination

7 Writing & Solving Systems of Equations Quiz Directions Solve each problem. Be sure to: 1. Identify the two variables in each situation 2. Write the system of equations 3. Show your work Name Date 1. The Browns scored 13 more points than the Saints. The total of their scores was 47. How many points did each team score? MATH IS FUN! 2. A company produces telephones at the rate of 600 per day. A customer survey indicates that the demand for phones with built in answering machines is twice as great as the demand for phones without the machines. If you are deciding the production quota for the day, how many phones with answering machines would you schedule for production? How many without answering machines would you make? 3. Sarah is the director of the Hoonah marching band. She must order 35 new uniforms for the band. There are usually five more girls than twice the number of boys in the band. How many uniforms of each type should she order for the band? 4. Mary s children decide to run a lemonade stand to earn some extra money. The cost to start the business is \$1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup, how many cups must Mary s children sell to make a profit? 5. At the Great Hair Barber Shop Nita and Joe do a total of 95 haircuts each week. If Nita does 16 fewer than twice as many as Joe, how many haircuts does each person do?

9 Writing & Solving Systems of Equations Quiz ANSWER KEY 1. The Browns scored 13 more points than the Saints. The total of their scores was 47. How many points did each team score? b = Browns score; s = Saints score b + s = 47 s + 13 = b s = 17 b = A company produces telephones at the rate of 600 per day. A customer survey indicates that the demand for phones with built in answering machines is twice as great as the demand for phones without the machines. If you are deciding the production quota for the day, how many phones with answering machines would you schedule for production? How many without answering machines would you make? t = regular telephones; a = phones with answering machines t + a = 600 t = 200 2t = a a = Sarah is the director of the Hoonah marching band. She must order 35 new uniforms for the band. There are usually five more girls than twice the number of boys in the band. How many uniforms of each type should she order for the band? b = number of boys uniforms; g = number of girls uniforms b + g = 35 g = 25 2b + 5 = g b = Mary s children decide to run a lemonade stand to earn some extra money. The cost to start the business is \$1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup, how many cups must Mary s children sell to make a profit? a = amount to break even; x = number of cups sold to break even \$ \$.06x = a x = 30 cups \$.10x = a a = \$3.00

11 9. A salesperson at an electronics store is given a choice of two different compensation plans. Plan A pays him a weekly salary of \$250 plus a commission of \$25 for each stereo sold. Plan B offers no salary but pays \$50 commission on each stereo sold. How many stereos must the salesperson sell to make the same amount of money with both plans? Write a paragraph answering the following questions: When is plan B the better plan? When is plan A the better plan? Which plan would you select and why? x = number of stereos sold; a = amount of money earned x = a x = 10 stereos 50x = a a = \$ ABLE Trucking Company has a job moving 21 tons of sand. The company has 8 drivers in the company and 2 types of trucks. One type of truck can haul 5 tons of sand and the other type of truck can haul 3 tons. Insurance requirements make it necessary for the trucks hauling 5 tons of gravel to have two drivers in the cab during operation. Three-ton trucks require only one driver. Using all available drivers, how many trucks of each size will be needed to move the sand in one trip? x = number of 5-ton trucks; y = number of 3-ton trucks 5x + 3y = 21 x = 3 2(x) + y = 8 y = 2

### Solving Systems of Linear Equations Putting it All Together

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