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Weekly Quiz 5 will be given after today’s lecture, during the last 30 minutes of class.

Weekly Quiz 5 will be given after today’s lecture, during the last 30 minutes of class. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials. Section 4.5, Part A Solving Problems with Systems of Linear Equations 1.

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Weekly Quiz 5 will be given after today’s lecture, during the last 30 minutes of class.

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  1. Weekly Quiz 5 will be given after today’s lecture, during the last 30 minutes of class.

  2. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

  3. Section 4.5, Part ASolving Problems with Systems of Linear Equations 1

  4. Steps in Solving Problems Involving Systems of Two Linear Equations in Two Variables: • Understand the problem. • Read and reread the problem. • Choose two variables to represent the two unknowns. • Translate the problem into two equations. • Solve the system of equations. • Interpret the results. • Check proposed solution in the problem. • State your conclusion. • Check proposed solution in the problem !!!!!

  5. Example One number is 4 more than twice the second number. Their total is 25. Find the numbers. 1. UNDERSTAND Read and reread the problem. Since we are looking for two numbers, we let x = first number y = second number continued

  6. One number is 4 more than twice the second number. continued 2. TRANSLATE x = 4 + 2y Their total is 25. x + y = 25 continued

  7. continued 3. SOLVE We are solving the system x = 4 + 2y x + y = 25 Using the substitution method, we substitute the solution for x from the first equation into the second equation. x + y = 25 (4 + 2y) + y = 25 Replace x with 4 + 2y. 4 + 3y = 25 Simplify. 3y = 21 Subtract 4 from both sides. y = 7 Divide both sides by 3. continued

  8. continued Now we substitute 7 for y into the first equation. x = 4 + 2y= 4 + 2(7) = 4 + 14 = 18 4. INTERPRET Check:Substitute x = 18 and y = 7 into both of the equations. First equation: x = 4 + 2y 18 = 4 + 2(7) True Second equation: x + y = 25 18 + 7 = 25 True State: The two numbers are 18 and 7.

  9. Example Hilton University Drama club sold 311 tickets for a play. Student tickets cost 50 cents each; non-student tickets cost $1.50. If the total receipts were $385.50, find how many tickets of each type were sold. 1. UNDERSTAND Read and reread the problem. Since we are looking for two numbers, we let s = the number of student tickets n = the number of non-student tickets continued

  10. Hilton University Drama club sold 311 tickets for a play. total receipts were $385.50 Admission for students continued 2. TRANSLATE s + n = 311 Admission for non-students Total receipts = + 1.50n 0.50s 385.50 continued

  11. continued 3. SOLVE We are solving the system s + n = 311 0.50s + 1.50n = 385.50 Since the equations are written in standard form (and we might like to get rid of the decimals anyway), we’ll solve by the addition/elimination method. (Substitution could be used instead, if you prefer to do it that way.) Question: If we wanted to eliminate s, what would we multiply the 0.50s in the second equation by to make it become -1s? Answer: Multiply the second equation by –2. s + n = 311 s + n = 311 –s – 3n = –771 –2(0.50s + 1.50n) = –2(385.50) –2n = –460 n = 230 continued

  12. continued Now we substitute 230 for n into the first equation to solve for s. s + n = 311 s + 230 = 311 s = 81 4. INTERPRET Check: Substitute s = 81 and n = 230 into both of the equations. s + n = 311First Equation 81+ 230 = 311 True 0.50s + 1.50n = 385.50Second Equation 0.50(81) + 1.50(230) = 385.50 40.50 + 345 = 385.50 True State: There were 81 student tickets and 230 non student tickets sold.

  13. The assignment on this material (HW 22) has 16 problems andis due at the start of class on Monday. Next week’s schedule: • Monday: Lecture on Section 4.5B • 16 more word problems due Tuesday (HW 23) • Tuesday: Review for Test 2 • Practice Test 2 due Wednesday • Wednesday:Take Test 2 (125 points) • Thursday: Advisement Day (no classes)

  14. There is a graphing problem on this quiz that will be graded by hand, so the maximum possible computer-graded score will be 7/8 (87.5%) until that question’s scored is entered. Please open your laptops, log in to the MyMathLab course web site, and open Weekly Quiz 5. • You have 30 minutes to finish this 8-question quiz. • If you finish the quiz problems in less than 30 minutes, remember to check your work and your online answers before submittingthe quiz. • After you submit your quiz, turn your worksheet in to the TA, and then you are free to leave. Your scratch work will be reviewed for possible partial credit points.

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