Solving Systems of Equations 11 Grade 7-Day Unit Plan
Tools Used: TI-83 graphing calculator (teacher) Casio graphing calculator (teacher) TV connection for Casio (teacher) Set of Casio calculators (students)

By: Nicole M. McCoy

Objectives of Unit:
The students will recognize the properties of systems of equations The students will discover four different methods to solving systems of equations The students will be able to choose the easiest method when solving a system
Standards addressed throughout lesson:

NCTM Standards

Numbers & Operations Algebra Problem Solving Communication Connections Representation

NYS Key Ideas

Key Idea 2- Number and Numeration Key Idea 3 Operations Key Idea 4 Modeling/Multiple Representation Key Idea 7 Patterns/Functions
Textbook Information: Publisher Scott Foresman Addison Wesley Title The University of Chicago School Mathematics Project Authors Senk, Thompson, Viktora, Usiskin, Abbel, Levin, Weinhold, Rubenstein, Jaskowiak, Flanders, Jakucyn, Pillsbury Chapter/pages Chapter 5/pages 279 - 311 Copyright 1998
Unit Overview Day 1 Solving Systems of Equations Graphically Day 2 Solving Systems of Equations Algebraically Using Substitution Day 3 Solving Systems of Equations Algebraically Using Linear Combinations Day 4 Review of Linear Combinations; Preview to Matrices Day 5 Solving Systems of Equations Using Matrices on the Casio Day 6 Solving Systems of Equations using any method word problems Day 7 More word problems and quiz
Day 1 Lesson: Solving systems of equations graphically Objectives o Students will recognize properties of systems of equations o Students will estimate solutions to systems by graphing Extra Materials o None Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have the students graph the following on separate graphs (provided by teacher): y = 3x - 5
y = 2x2 xy = 4 This will determine who knows how to use their graphing calculator and who needs more help/practice.
Main Activity As a class, we will discuss how to find the solution to a system of linear equations using the graphs of the lines. NOTE This method can only be used if solving for 1 or 2 variables due to the limited powers (no 3-D capabilities on the graphing calculators) This will be mentioned to the students early in the lesson. The students will find the solution(s) to the following systems while working in groups. Then, each group will present one system and show how they arrived at the solution(s). 1 y = x - 7 y = 3 x + 13 y = x +1 1. 2. 3. 2 y = -2 x + 5 y = x +1 x - 2 y = -2
9 x - y = 12 4. y = 9x + 6 y + 3 = 7x 5. y = 6x + 2 y = 5x 6. y = -3 x + 1
Closing Activity Have the students write a brief sentence or two answering this question: In example 4, there was no solution because the lines were parallel. Give a situation where there would be an infinite amount of solutions to a system of linear equations. Think about the parallel lines example. Homework Page 283 # 10-12, 15 4
Day 2 Lesson: Solving systems of equations algebraically using substitution Objectives o Students will solve 2x2 and 3x3 systems using substitution o Students will recognize properties of systems of equations Extra Materials o Class set of Lesson Master 5-3 B Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have students solve the following: If y = -1, solve the following equations for x: 1. x = -2y + 4 2. 4x + 3y = 9 3. 8 = x + y 2 Answers: 1. x=6 2. x=3 3. x=7 Main Activity Students will learn how to solve systems of equations using the substitution method and Lesson Master 5-3 B. Together we will discuss how to use substitution to solve for the variables. The teacher will put the following example on the board: 5=2+3 4+1=5 Ask the students how to change this from two different equations to one equation that is equivalent. Answer: 2 + 3 = 4 + 1; because they both equal 5, they must both be equal to each other. Discuss when and why we use substitution. - It is used when we have more than 1 unknown (variable) and one of the equations can be solved for 1 variable. Then we substitute that variables value in terms of the other variable(s) into the other equation. Discuss how to use substitution. - This is when we, as a class, will work through the odd numbered problems on the Lesson Master 5-3 B. The students will solve 2x2 and 3x3 systems using substitution.

Closing Activity On a half sheet of paper students will comment on the substitution method for solving systems of equations. They will include: - When and why we use substitution - How to use substitution - If they prefer graphing the two lines or solving algebraically and why This will be the Ticket out of Class and each student needs to hand the teacher a paper to exit the room. (NOTE: No late passes will be allowed if student refuses!) Homework Finish worksheet
Lesson Master 5-3B In 1-8, use substitution to solve the system. Then check. 1.

y = x - 7 y = -2 x + 5

y = 3 x + 13 y = x +1
3m - 2n = 1 21m - 6n = 11

xy = 4 x = -4 y

.25 x +.1 y = 78 7.5 y - 1.5 x = 990
4a + 6b - 3c = -26 b = a + 3 c = -4a
xy + z = 10 z = - x + 1 y = x +1

1 y = x + x - 2 y = -2

Lesson Master 5-3B (Answer Key) In 1-8, use substitution to solve the system. Then check. 1.

x=4; y=-3

x=-6; y=-5

m=2/3; n=1/2

x=-4; y=1 x=4; y=-1

x=240; y=180

a=-2; b=1; c=8
infinitely many solutions
x=3; y=4; z=-2 x=-3; y=-4; z=2
Day 3 Lesson: Solving systems of equations algebraically using linear combinations Objectives o Students will solve 2x2 and 3x3 systems using linear combinations o Students will recognize properties of systems of equations Extra Materials o Class set of Lesson Master 5-4 B Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have students solve the following: y = 2x + 3 4x + 3y = 29 Answers: x=2 y=7 Main Activity Students will learn how to solve systems of equations using the linear combinations method and Lesson Master 5-4 B. Together we will discuss how to use linear combinations to solve for the variables. The teacher will put this example on the board: 4x 6y = 3 2x + 12y = -6 Ask the following questions: 1. How would we get the coefficients of the xs to be the same number with opposite signs? Answer: Multiply the 2x by -2 2. How would we get the coefficients of the ys to be the same number with opposite signs? Answer: Multiply the 6y by 2 Discuss when and why we use linear combinations. - It is used when we are not able to solve for one variable easily (or at all) and/or one equations variable is a multiple of the others. Discuss how to use linear combinations. - This is when, as a class, we will do the problems together on Lesson Master 5-4 B. Students will solve 2x2 and 3x3 systems using linear combinations. Closing Activity On a half sheet of paper students will discuss which algebraic method of solving the systems of equations they would use to solve the following problems and why. 1. 6x + 12y = 5 (substitution) 2. x + y = 9 (linear combinations) y = 2 10x 2x y = 2 9

2x + 3y + z = 13 (linear combinations) 5x 2y 4z = 7 4x + 5y + 3z = 25
y = 3x (substitution) xy = 48
This will be the Ticket out of Class and each student needs to hand the teacher a paper to exit the room. (NOTE: No late passes will be allowed if student refuses!) Homework Finish worksheet 5-4 B
Lesson Master 5-4B In 1-8, use linear combinations to solve the system. Then check. 1.

4 x + y = -x + 2 y = -15

4 x + 3 y = 2.x - 2 y = 2.1
2a + b - 5c = -21 a + 2b - 2c = -15 a - 4b + c = 18
8m - 2n = -16 2m -.5n = -4
12 x 2 - 5 y 2 = 523 x + 2 y 2 = 482
4 x + 5 y = -x + 10 y = -20

x - y = -8 1 x + 4 y =

d + 9e - f = 13 3d + e + 2 f = -7 2d + 2e + 2 f = -6
Lesson Master 5-4B Answer Key In 1-8, use linear combinations to solve the system. Then check. 1.

x=-1.5; y=-6

x=.5; y=.2

a=-1; b=-4; c=3

x=8; y=7 x=8; y=-7 x=-8; y=7 x=-8; y=-7

no solution

1 x - y = - 1 x + 4 y =

x=-12; y=5

d=0; e=1; f=-4
Day 4 Lesson: Review of Linear Combinations and Solving systems of equations algebraically using matrices on graphing calculator Objectives o Students will solve 2x2 and 3x3 systems using matrices on graphing calculator o Students will recognize properties of systems of equations Extra Materials o Students worksheets from previous class day (Lesson Master 5-4 B) Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have students solve the following: Solve the following system of equations using linear combinations: 2x y = 4 Answer: x = 4 -x + 3y = 8 y=4 Main Activity Students will review how to use the linear combination method to solve systems of equations. As a class, we will go over the homework problems that caused the students difficulty. After all homework questions have been answered and the students have done a 3x3 system, we will quickly set up the matrix method on the calculators. STEPS: Turn calculator on to the main menu. Go to EQUA and hit EXE. This is a simultaneous process, so hit F1 for simultaneous. Next, we need to enter the number of unknowns. For a 3x3 we will have 3 unknowns (variables). Enter in all of the coefficients and the constants as prompted on the screen. After all the numbers are entered, hit F1 to solve. This will give the answer matrix to the 3x3 system we entered. Ask the students which way they prefer. I guarantee it will be the matrix method. Closing Activity Have the students try another system from their homework on the calculator. Have them do as many as time will allow. Discuss with them quickly that this will not however be accepted as full credit work on an exam. There is some work involved and we will discuss that tomorrow.

Day 5 Lesson: Solving systems of equations algebraically using matrices on the calculator and why it works Objectives o Students will solve 2x2 and 3x3 systems using matrices on the calculator o Students will recognize properties of systems of equations o Students will understand the steps involved to solve systems using the matrix method Extra Materials o Class set of worksheets Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have students solve the following system using the matrix method: 2x 2y + 4z = 7 Answer: x = -33 -4x + 2y 3z = 14 y = -126.5 x + 4y -12z = 1 z = -45 Main Activity Have the students learn how the matrix method works without actually showing them how to use a matrix. We will as a class go through the steps to solving a system using the matrix method. Step 1: Change system of equations to matrix equation:
2x 2y + 4z = 7 - 4x + 2y 3z = 14 x + 4y - 12z = 1
This system becomes the following matrix
coefficient matrix 2 -- -3 - 12
constant matrix x 7 y = 14 z 1
variable matrix Step 2: Label the matrices:
2 -- -3 - 12 A x 7 y = 14 z 1 B
Step 3: Multiply [A] x [A] so that all we have on the left side of the equation is the variable because we have an equation, we need to multiply [A] x [B ] on the right So we now have:
x [A] x [A] y = [A]-1 x [B] z -1 Step 4: [A] x [A] cancel out to become the identity matrix (essentially 1) and so we are now

matrix. And,

side of the equation.

left with:

x y = [A]-1 x [B ], where [A]-1 x [B ] is the answer matrix. z
This is enough work to show for full credit. Now, the students will put numbers into the calculator to get the answer matrix. They will work on the worksheets in pairs and solve for the variables, showing all of their work. Closing Activity Explain in your own words why [A] x [A] cancels out (becomes 1). Give an example using numbers. Example Answer: 2 = 1 , where is the inverse and 1 is the identity. Homework Finish worksheet
Name _____________________________________

Date ________________

Solving Systems of Equations using Matrices
Directions: Solve the following systems of equations using the matrix method on your calculator. 1) 3x y + 4z = -17 4x + 3y - 5z = 4 x + 6y + 2z = -6 1) Number of unknowns ________
m+ n+ p+ q =7 -2m + 4n p + 3q = 1 4m 2n + 4p + q = 4 -m + 2n 3p 2q = 8
2) Number of unknowns ________
s+ t u =5 2s - 5t + 3u = 10 -s + 6t 7u = 2
3) Number of unknowns ________
a + 2b + 3c + 4d + 5e = 6 -a 3b 2c 5d 4e = 12 4a + 7b 7c + 8d e = -2 -3a + 2b + 8c 2e = 14 6a 5b 2c + d 4e = 0
4) Number of unknowns ________
2h j + 4k 2m = 23 4h + 2j k + 3m = -1 h 5j + 8k 4m = 19 -3h + j 2k = -6

5) Number of unknowns _________
Name _______Answer Key_________________________
Directions: Solve the following systems of equations using the matrix method on your calculator. 1) 3x y + 4z = -17 4x + 3y - 5z = 4 x + 6y + 2z = -6 x = -2.2731; y =.2098; z = -2.4927 m+ n+ p+ q =7 -2m + 4n p + 3q = 1 4m 2n + 4p + q = 4 -m + 2n 3p 2q = 8 m = -3; n = 9; p = 11; q = -10 s+ t u =5 2s - 5t + 3u = 10 -s + 6t 7u = 2 s = 4 1/3; t = -1 2/3; u = -2 1/3 1) Number of unknowns ____3____
2) Number of unknowns ____4____
3) Number of unknowns _____3___
a + 2b + 3c + 4d + 5e = 6 4) Number of unknowns _____5___ -a 3b 2c 5d 4e = 12 4a + 7b 7c + 8d e = -2 -3a + 2b + 8c 2e = 14 6a 5b 2c + d 4e = 0 a = 32.4846; b = 25.9596; c = 8.4963; d = -31.2455; e = 4.2179 2h j + 4k 2m = 23 4h + 2j k + 3m = -1 h 5j + 8k 4m = 19 -3h + j 2k = -6 h = 2.4285; j = 6.5714; k = 2.6428; m = -7.0714 5) Number of unknowns _____4____
Day 6 Lesson: Given word problems, change into systems of equations and solve for the variables Objectives o Students will change word problems into systems of equations and solve for variables o Students will solve 2x2 and 3x3 systems using matrices on the calculator o Students will recognize properties of systems of equations Extra Materials o Class set of word problem worksheets Opening Activity Student Bellwork: The students have 5 minutes to complete the following problem. The students will then pass the paper to a different student and they will correct each others papers. The teacher will collect the papers after we correct them as a class. Have students solve the following system using whichever method they choose: -3x + 4y = -2 Answers: x = -2.8 -x + 2y = 6 y = 1.6 Main Activity Given word problems, students will change into a system of equations and then solve for the variables. We will do some examples as a class, and some examples will be done as pairs. Students can use any method that we have learned to solve the systems. Closing Activity Given this system, try to write a word problem that would make sense. You dont need to solve the system, just write a word problem. x = y + 10 7x 3y = 25.60 Homework Finish worksheet on word problems.
Worksheet on Word Problems 1. Five yards of fabric and three spools of thread cost $40.12. Two yards of the same fabric and ten spools of the same thread cost $23.88. Find the cost of a yard of fabric and the cost of a spool of thread. Fabric _______________ Thread __________________
Half a watermelon and a half pound of cherries cost $3.09. A whole watermelon and two pounds of cherries cost $8.16. a. Write a system of equations that can be used to find the cost of each type of fruit.

Solve the system to find the cost of each type of fruit. Cherries ___________________________
Watermelon ____________________
Two apples and six plums provide 300 calories. Three apples and five plums provide 350 calories. How many calories are provided by five apples and eight plums?_________________________
At Wet Pets, a starter aquarium kit costs $15 plus $.60 per fish. At Gills and Frills, the same kit is $13 plus $.80 per fish. a. Give an equation for the cost c of f fish at each store. Wet Pets ___________________ b. Gills and Frills ________________________
For what number of fish is the cost the same at the two stores? ______________________
For the Summer Rock Festival, there is one price for students, one for adults, and another for senior citizens. The Rueda family bought 3 student tickets and 2 adult tickets for $104. The Cosentinos bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Cragins bought 2 of each for $126. a. b. Write a system of equations that can be used to find the cost of each ticket Solve the system to find the cost of each ticket.
Students _______________ Adults _________________ Senior Citizens ___________________
A bicycle, three tricycles, and a unicycle cost $561. Seven bicycles and a tricycle cost $906. Five unicycles, two bicycles, and seven tricycles cost $1758. a. Set up a system of equations that can be used to find the cost of each item. b. Solve the system to find the cost of each type of cycle.
Bicycle _________________ Tricycle ________________ Unicycle ________________
Worksheet on Word Problems Answer Key 1. Five yards of fabric and three spools of thread cost $40.12. Two yards of the same fabric and ten spools of the same thread cost $23.88. Find the cost of a yard of fabric and the cost of a spool of thread. Fabric ____$7.49___________ 5f + 3t = 40.12 2f + 10t = 23.88 Thread ____$.89______________
Half a watermelon and a half pound of cherries cost $3.09. A whole watermelon and two pounds of cherries cost $8.16. a. Write a system of equations that can be used to find the cost of each type of fruit.5w +.5c = 3.09 w + 2c = 8.16 b. Solve the system to find the cost of each type of fruit.
Watermelon ______$4.20______________ Cherries ______$1.98 per lb._______________
Two apples and six plums provide 300 calories. Three apples and five plums provide 350 calories. How many calories are provided by five apples and eight plums?_______575 calories_________ 2a + 6p = 300 3a + 5p = 350 a = 75 p = 25 5a + 8p = ? 5(75) + 8(25) = 575

At Wet Pets, a starter aquarium kit costs $15 plus $.60 per fish. At Gills and Frills, the same kit is $13 plus $.80 per fish. a. Give an equation for the cost c of f fish at each store. Wet Pets ___C = 15 +.60f________ Gills and Frills ___C = 13 +.80f_________ b. For what number of fish is the cost the same at the two stores? ______10 fish________
For the Summer Rock Festival, there is one price for students, one for adults, and another for senior citizens. The Rueda family bought 3 student tickets and 2 adult tickets for $104. The Cosentinos bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Cragins bought 2 of each for $126. a. Write a system of equations that can be used to find the cost of each ticket 3s + 2a = 104 5s + a + 2c = 155 2s + 2a + 2c = 126 Solve the system to find the cost of each ticket.
Students ___$18_________ Adults ____$25__________ Senior Citizens ____$20____________
A bicycle, three tricycles, and a unicycle cost $561. Seven bicycles and a tricycle cost $906. Five unicycles, two bicycles, and seven tricycles cost $1758. a. Set up a system of equations that can be used to find the cost of each item. b + 3t + u = 561 7b + t = 906 2b + 7t + 5u = 1758 b. Solve the system to find the cost of each type of cycle. Bicycle ____ $117________ Tricycle ____ $87________ Unicycle ___ $183_________
Day 7 Lesson: Given word problems, change into systems of equations and solve for the variables Quiz on Sections 5-2 to 5-4 Objectives o Students will change word problems into systems of equations and solve for variables o Students will solve 2x2 and 3x3 systems using matrices on the calculator o Students will recognize properties of systems of equations Extra Materials o Class set of quizzes Opening Activity Quiz on Sections 5-2, 5-3, 5-4, 5-6 and including word problems Main Activity As a class, we will review how to change a word problem into a system of equations. We will go over in detail the previous nights homework sheet answering any and all questions that may arise. The students will first share their answers on the board: o One student will put the system of equations on the board o Another student will solve the problem for the necessary information This method will be repeated for each homework problem. Closing Activity Have students change this word problem into a system of 2 equations and hand in before exiting the classroom: At the zoo, Jay bought 3 slices of vegetable pizza and 1 small lemonade for $5.40. Terri paid $4.80 for 2 slices of vegetable pizza and 2 small lemonades. Answer: 3P + 1L = 5.40 2P + 2L = 4.80

Name ________________________________________ Chapter Quiz
Date ___________________ Advanced Algebra
In questions 1 & 2, solve the system graphically or algebraically. Show all work. 1.
12 s - 8t = 56 5s + 3t = - x + 4 y = -7 y = 3x + 6

1. _____________________

2. _____________________
3. Consider the system graphed below. How many solutions does the system have? 3. ______________________
In questions 4 & 5, refer the the following situation: At Federal Rent-A-Car, the cost of a one-day rental of a midsize car is $45 plus $0.27 per mile driven. At Ready Rentals, the cost is $27 per day plus $0.36 per mile driven. 4. Let x = the number of miles driven and y = the cost of a one-day rental with x miles driven. Set up a system of two equations to describe this situation. 5. a. For what number of miles driven will the cost of a one-day rental be the same at Federal Rent-A-Car and at Ready Rental. b. What is the cost for this number of miles driven? 4. ________________________ ________________________
5. a. ______________________
b. ______________________

*Extra Credit*

kx + 2 y = 12 For what value of k does 9 x + 2 y = 8 Justify your answer.

have no solution?

__________________________________________________________________________________________ __________________________________________________________________________________________ 24
Name ___________Answer Key_____________________ Date ___________________ Chapter Quiz Advanced Algebra In questions 1 & 2, solve the system graphically or algebraically. Show all work. 1.
1. __s = 2; t = -4 ____________
2. ___x = -1; y = 3__________
3. Consider the system graphed below. How many solutions does the system have? 3. ________2 solutions____
In questions 4 & 5, refer the the following situation: At Federal Rent-A-Car, the cost of a one-day rental of a midsize car is $45 plus $0.27 per mile driven. At Ready Rentals, the cost is $27 per day plus $0.36 per mile driven. 4. Let x = the number of miles driven and y = the cost of a one-day rental with x miles driven. Set up a system of two equations to describe this situation. 5. a. For what number of miles driven will the cost of a one-day rental be the same at Federal Rent-A-Car and at Ready Rental. b. What is the cost for this number of miles driven? 4. ____y=45+.27x___________ ____y=27+.36x___________

5. a. ___200 miles___________
b. ___$99.00_____________
____When k = 9, there is no solution because when you perform linear combinations on the system you get that 0=4 and this will never be true, therefore the lines are parallel, and no solution exists. _____________________ 25

Casio SE-S10 M Setup and Programming Steps Cash Register Support 011-SE-S10 M SETUP
1. Turn PGM key to PGM mode 2. Plug in Cash Register into wall socket 3. Open the printer lit and insert batteries under the paper roll a. Batteries are not supplied with Cash Register 4. Drop the Thermal Roll inside the paper slot

SETUP TIME AND DATE

1. 2. 3. 4. 5. Enter 0 and press Cash English When the display shows blinking 0 Enter 2 Digits (Day) & press Cash Enter 2 Digits (Month) & press Cash Enter 2 Digits (Year) Cash Register will Reset Automatically
NB: By pressing AC/C key, this procedure returns one by one 1. When the display shows a blinking 0 2. Enter 2 Digits (Hours) & press Cash 3. Enter 2 Digits (Minutes) & press Cash Now a Receipt will be printed with the Date & Time Programmed
BASIC OPERATION - SE-S10M
1. 2. 3. 4. 5. Turn mode switch to REG Type in the amount of the item and press the department button 1-5 If you are done with the sale press subtotal and then total will be on screed. Type in the amount that the customer gives you and press cash. This will finalize your transaction and present Customer Change

SETUP OF PLUS

1. 2. 3. 4. 5. 6. PLU Price Turn the mode switch to PGM Type in the first PLU number and press the PLU button Type in the price and press cash You can keep on doing this until all your 500 PLUS are entered To save all the prices press subtotal Turn the mode switch back to REG PLU Descriptions Turn the mode switch to PGM Enter 2 & press Subtotal Enter PLU Number & press the PLU KEY Enter Character SMS style & Press 00 & Press Cash Press Subtotal To Save

1. 2. 3. 4. 5.

STEPS ON USING PLUS
1. 2. 3. 6. 7. 4. Turn mode switch to REG Enter the PLU number of the item you want to sell and press the PLU button This will ring up the price on the screen If you are done with the sale press subtotal and then total will be on screed. Type in the amount that the customer gives you and press cash. This will finalize your transaction and present Customer Change

Department Programming

1. 2. 3. 4. 5. 6. Descriptions Turn mode switch to PGM Enter 2 & press Subtotal Press Dept Key Enter Descriptions Press 00 for next letter When done press Cash Press Subtotal to save
Link PLUs to Departments 1. 2. 3. 4. Turn Key to PGM and enter 3 & press Subtotal Enter PLU number & Press PLU Key Enter 1 for Dept 1 or 2 for Dept 2 & Press Cash Press Subtotal to Save
PROGRAMMING TAX ON THE SLIP
1. 2. 3. 4. 5. 6. Turn mode switch to PGM Enter 3 and press subtotal Enter 0125 and press subtotal Enter 14 & press cash Enter 5003 & press cash Enter Subtotal to save
Tax on Departments 7. Press 1 and Subtotal 8. Press TAX PGM Key Once 9. Enter TAX Rate and press the Department key 10. Do step 9 until all your departments are set with Tax 11. Press subtotal to save Program Tax on Cash Button 12. Press 3 subtotal 13. Press 0326 subtotal 14. Press 3 cash 15. Press subtotal
Programming Receipt Message
1. Turn mode switch to PGM 2. Enter 2 & press Subtotal 3. Enter 2 & press CH key This will take you to the first record 4. Enter Receipt Message description & press Cash 5. Enter 3 & press CH key This will take you to the second record 6. Enter Receipt Message description & press Cash 7. Enter 4 & press CH key This will take you to the third record 8. Enter Receipt Message description & press Cash 9. Enter 5 & press CH key This will take you to the fourth record 10. Enter Receipt Message description & press Cash 11. Press Subtotal to save

DOING A DAY END REPORT

1. Turn mode switch to Z mode 2. Press Cash Amount This Z Reports will clear your Day End Totals but will Not Clear your monthly total.

DOING A MONTH-END REPORT

1. 2. 3. 4. Turn mode switch to Z mode Enter 10 Press Cash Amount This Z Monthly reports clears all totals for the month.