Weekly Quiz 5 will be given after today’s lecture,

during the last 30 minutes of class.

1

Please

CLOSE

YOUR LAPTOPS,and turn off and put away your

cell phones,

and get out your note-taking materials.

Section 4.5, Part ASolving Problems with

Systems of Linear Equations 1

3

Steps in Solving Problems Involving Systems of Two Linear Equations in Two

Variables:1) Understand the problem.

• Read and reread the problem.• Choose two variables to represent the two

unknowns.

2) Translate the problem into two equations.

3) Solve the system of equations.

4) Interpret the results.• Check proposed solution in the problem.• State your conclusion.

Check proposed solution in the problem !!!!!

Example

continued

One number is 4 more than twice the second number. Their total is 25. Find the numbers.

Read and reread the problem.

Since we are looking for two numbers, we let

x = first number

y = second number

1. UNDERSTAND

continued

2. TRANSLATE

continued

One number is 4 more than twice the second number.

x = 4 + 2y

Their total is 25.

x + y = 25

3. SOLVE

continued

continued

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.

We are solving the system x = 4 + 2yx + y = 25

4. INTERPRET

continued

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.

Now we substitute 7 for y into the first equation.

x = 4 + 2y = 4 + 2(7) = 4 + 14 = 18

Example

continued

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 lets = the number of student ticketsn = the number of non-student tickets

continued

2. TRANSLATE

Hilton University Drama club sold 311 tickets for a play.

s + n = 311

total receipts were $385.50

0.50s

Total receipts

= 385.50

Admission for students

1.50n

Admission for non-students

+

continued

3. SOLVE

continued

We are solving the system s + n = 3110.50s + 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

–2(0.50s + 1.50n) = –2(385.50)

s + n = 311

–s – 3n = –771

–2n = –460 n = 230

continued

4. INTERPRET

Check: Substitute s = 81 and n = 230 into both of the equations. s + n = 311 First Equation

81 + 230 = 311 True

0.50s + 1.50n = 385.50 Second Equation

40.50 + 345 = 385.50 True

0.50(81) + 1.50(230) = 385.50

State: There were 81 student tickets and 230 non student tickets sold.

Now we substitute 230 for n into the first equation to solve for s. s + n = 311

s + 230 = 311

s = 81

continued

The assignment on this material (HW 22) has 16 problems and is 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)

Please open your laptops, log in to the MyMathLab course web site, and open Weekly Quiz 5.

• 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.

• 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 submitting the 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.