Grp 11 SQQM2023 Project

Healthy JUN 2022
food choices
are happy
food choices

HEALTH IS WEALTH

AUTHORS

Chloe Lee Yue-Ki Healthy food choices are happy food
284719 choices
Jun 2022
Tin Wei Won
284860 Editor
Chloe Lee Yue-Ki 
Foo Jia En Lee Xue Lin 
284885 Tin Wei Won

Design
Foo Jia En
Ooi Xin Yee

Information Contributors
Foo Jia En
Tin Wei Won
Ooi Xin Yee
Chloe Lee Yue-Ki
Lee Xue Lin

Lee Xue Lin Subscriptions
285888 Visit www.3kuum.com

Ooi Xin Yee www.3kuum.com
286871 [email protected]

Published by Persatuan 3K University Utara
Malaysia

TABLE OF CONTENTS

CONTENTS 04
Background of UUM 05
Problem / Issue 06
Introduction of Organization 07
Meeting & Survey 09
Problem Solution
Common Food Choices in UUM 10
Reflection
Reference The Variables 13
Appendix Our Equations &ScoRtleansdu, lItcseland and Ireland 14

What is The System of Linear 17
Equation
20
Ways to Solve Systems of 21
Linear Equations

Conclusion

Sean Fraser

23
28
30

Visit
WWW.3KUUM.COM

Background of UUM

ADDRESS: SINTOK, 06010 BUKIT KAYU HITAM, KEDAH
PHONE: 04-928 4000

  UUM is an abbreviation for Universiti Utara Malaysia. On February 16,
1984, it was founded and became the sixth university in Malaysia. The
main campus of UUM is located in Sintok, Kedah and there is a second
campus in Kuala Lumpur. It is a management university. It offered a wide
range of courses, including economics, finance, accountancy, business
mathematics, and many more. In UUM, there are three primary colleges
which are CAS, COB and COLGIS. Besides, there are a lot of organizations
which are conducted by students of UUM. One of the famous organization
is Keselamatan, kebersihan, kesihatan (3K UUM).

04 | JUN 2022

Introduction
of
Organization

Our organisation is known as Keselamatan,
kebersihan, kesihatan (3K UUM). This organisation
aims to spread the awareness of “The Importance
of Nutrition”. In UUM, we discovered that many of
the food stalls sell unhealthy food. Students in
UUM will prefer unhealthy foods over nutritious
ones like vegetables and fruits. As a result, they
will suffer from a lack of nourishment. Besides
that, obesity will also result from consuming too
many calories. To overcome this problem, we
designed an app to calculate the grams of food
that students should consume based on the
suggested calories.

JUN 2022 | 05

Problem/ Issue Calories are the amount of energy released when
your body breaks down. According to the World

Health Organization (WHO), energy intake

(calories) should be in balance with energy

L A C K O F N O U R I S H M E N T expenditure. Over-consuming calories will lead

AND OBESITY to obesity. Obesity and malnutrition both
increase the risk of noncommunicable

diseases(NCDs) such as stroke, diabetes and

cancer. WHO encourages people to consume

more vegetables and fruits to prevent these

diseases. People should consume 400g or more of

vegetables and fruits each day in order to

maintain a balanced diet.

06 | JUN 2022

Meeting & Survey

The 3K club had a meeting in May to discuss the issue of the
UUM students' unhealthy diet. Club managers Chloe, Deb, Xue
Lin and Wei Won as well as club president, Jane were present at
the meeting. After surveying about 150 UUM students through
google form over the past few months, we have concluded that the
majority of respondents have an unbalanced diet and are eager to
correct it. As a result, in this project, we are going to assist these
respondents to overcome the problem by create an application

about the system of linear equations.

JUN 20221 | 07

Meeting & Survey

MAY 2022

Meetin
g and Survey Results

63% 32% 5%

Very concerned Concerned Not concerned

According to the result of survey,
63% of meeting planners and respondents are VERY
CONCERNED, 32% are CONCERNED and 5% are NOT

CONCERNED with 'the Lack of nourishment and
obesity' situation.

08 | JUN 20221

Problem Solution

USING THE SYSTEM OF
LINEAR EQUATION

To solve the issue we faced,
members of 3K UUM decided create
an application about the system of
linear equations.
When creating this app, we
randomly selected 7 common food
to form several equations. The 7
common foods are burger, rice,
fried chicken, pizza, meat,
vegetables and fruits. We make a
system of linear equation according
to the calories of the food.

JUN 2022 | 09

COMMON FOOD
CHOICES
IN UUM

7 TYPES OF FOOD

10 | JUN 20221

JUN 2022 | 11

Burger
354 calories per 100 grams

Fried chicken
246 calories per 100 grams

Rice
130 calories per 100 grams

THE SEVEN



COMMON FOOD

12 | JUN 20221

Pizza
266 calories per 100 grams




Meat
143 calories per 100 grams




Vegetable
65 calories per 100 grams




Fruit
52 calories per 100 grams

THE
VARIABLES

XXXX

The calories of the food are recorded according to the
research of U.S. DEPARTMENT OF AGRICULTURE

(USDA)

13 | JUN 2022

OUR EQUATIONS &
RESULTS

We randomly selected the daily meals of 4 respondents
from the survey, and we can use a linear equation to

calculate the calories consumed by the 4 respondents per
meal. Women consume 533-800 calories per person and
men 667-1000 calories. So, we get the average total intake

per meal, which is 666.5 calories for women and 833.5
calories for men. Therefore, through this app, we can help

UUM students improve their diet, and even if they eat
what they like, they can control the amount of food within

the prescribed range.

Respondents:
Siti:
Burger + fried chicken
354 x1 + 246 x3 = 666.5

Mei Ling:
Rice + Meat + Vegetable
130 x2+ 143 x5 + 65 x6 = 666.5

Ali:
Fried chicken + Pizza + Nugget
246 x3 + 266 x4 + 296 x7 = 833.5

Mutu:
Rice + Fried chicken + Nugget
130 x2 + 246 x3 + 296 x7 = 833.5

14 | JUN 2022

OUR EQUATIONS &

RESULTS

For example, if Siti eats burgers and fried chicken. x5, x6 and x7 will be
equal to 0. So Burger = 1.411 and x3 = 0.6789, which means Siti can eat 141.1
grams of burger and 67.89 grams of fried chicken (1 calorie per 100 grams)

to ensure her total calories are within the set range of 666.3 calories.

15 | JUN 2022

THE
SECRET RELATIONSHIP
BETWEEN FOOD AND
LINEAR EQUATION

X+Y=6 UNIQUE ?
3Y + 4Z = 7 INFINITE ?
X+Y+Z=0 NO SOLUTION ?

16 | JUN 2022

WHAT IS THE
SYSTEM OF LINEAR

EQUATIONS ?

07

A system of linear equation or linear When the system of linear
system is when we have more than 2 equations has no solution, the
linear equations which includes the graph of the linear equations are
same variables. parallel to each other. Whereas if
the system of linear equations is an
For example, we have unique solution, the graph of the
linear equations intersect with each
x + 2y + z = 6 other. Lastly, if the solution of the
x+ y=3 linear equations is infinite, the
z=1 graph of the linear equations are
straight lines that overlaps each
x,y,z are variables. The solution other. If there is no solution to the
of the system is as follows , system, then it is inconsistent and if
there is at least one solution to the
(x , y , z) = (1 , 2 , 1) system, the system is said to be
consistent
There are 3 possibilities for
solutions to the system

no solution (unique
exactly one solution
solution)
many solution (infinite)

17 | JUN 2022

Intersecting lines Parallel lines Same lines
- One common point - No common point - Many solution
- Unique solution - No solution

There are two ways to solve system of linear equations for square matrix,
Cramer's Rule and Inverse Method. For Cramer's Rule, it is a formula for the
solution of a system of linear equations with many equations that includes
unknown variables.

Cramer's Rule Formula :

x= Dx y= Dy z= Dz
D D D

For inverse matrix, let A be the coefficient matrix, X be the variable matrix
and B be the constant matrix.

Inverse Method :

AX = B where A-1 = 1
X = A-1 B adj (A)

det (A)

18 | JUN 2022

Next, we can solve systems of equations by using linear algebra techniques.
A matrix is known to be reduced row-echelon form if it satisfies all 4
conditions. However, the matrix is in a row-echelon form if it satisfies at least
1 condition.

1. If any rows have all zeros, it must be at the bottom of the matrix
2.If the row does not have all zeros then its first non-zero entry must be 1

(leading 1)
3. If any 2 consecutive rows, contain no all zeros, the leading 1 of the

lower row is to the right of the leading 1 of the higher row
4. If a column begins with a 1, all subsequent entries in that column are

zero.

If further work is needed to get the solution, we can use Gauss Elimination
and Gauss Jordan elimination. Gauss Elimination is reducing the augmented
matrix to reduced row-echelon form. Whereas Gauss Jordan elimination is
reducing the augmented matrix to row-echelon form.

19 | JUN 2022

LINEAR
EQUATION

WAYS TO SOLVE
SYSTEMS OF
LINEAR EQUATIONS

Methods:
1.Gaussian Elimination
2.Cramer's Rule
3.Elementary Row Operation (ERO)

Since elementary row operations (ERO) are based on row to row’s, column
to column’s, or equation to equation's transformations, this approach will
require us to perform many operations when we encounter more
important equations or matrices. Elementary row operations (ERO) can be
used to transform the coefficient matrix into the desired form that helps in
obtaining the solution. For example, the coefficient matrix can be brought
to upper triangular form (or row trapezoid form) 3 by basic row operations.
In the upper triangular form, all elements along and above the diagonal are
non-zero, and all elements below the diagonal elements are zero. The
coefficient matrix can be brought into diagonal form (or simplified
trapezoidal form) by basic row operations. In this case, only the diagonal
elements are non-zero, and the diagonal elements are zero.

20 | JUN 2022

THE Jun
2022

Con
clusion

In this project, the aim was to calculate the calories taken by
UUM students in the café in a day using linear equations.
According to the scenario, we had 7 menus as the
unknowns, and we used these 7 unknowns to create a linear
system with 4 equations. Based on our project’s aim, we
need to find out the amount of calorie intake by UUM
students with these 7 menus by using the linear systems
that we had created.

As we know, there are 4 methods to solve the
system of linear equations which were
Cramer’s Rule, Inverse Method, Gauss
Elimination and Gauss Jordan Elimination. For
Cramer’s Rule, it is used for solving a linear
system with the same number of variables as
unknowns and is only used for a linear system
that had a unique solution.

JUN 20221 | 21

THE Jun
2022

Con
clusion

M oreover, Gauss Elimination and Gauss Jordan
Elimination can be used to solve systems of
complex linear equations. After performing Gauss
Elimination on a matrix, the result is in row-echelon
form, while the result after the Gauss Jordan
Elimination is in reduced row-echelon form.
(Stephen Andrilli and David Hecker, 2016).

However, Cramer’s Rule and Inverse Method
only can use for a square matrix. Therefore, we
use the Gauss Elimination Method method to
solve our linear systems since we decided to
have 4 equations with 7 unknowns. After doing
the calculation, we got 3 free variables in the
linear system which were x5, x6 and x7.
According to the results, we can say that the
system had infinitely many solutions and it was
said to be consistent.

22 | JUN 2022

REFLE Chloe Lee Yue-Ki
CTION 284719

While doing this project, I can learn how to apply
systems of linear equations to our daily life. For
example in the field of physics, chemistry, economics,
business, engineering, healthcare and so on. In doing
this project, I did a lot of research to understand the
concept of systems of linear equations and study a lot
to make sure I had enough knowledge to apply these

equations.



In this project, I successfully identified an application
and real-world problem for solving linear systems
equation by formulating a linear system with
at least seven variables in the equation to solve the
problem. In solving this problem, we used Elementary
Row Operations (ERO) method that I have learn in
linear algebra SQQM2023 course. At the end of this
project, I can determine the amount of each food
required for each meal to achieve a balanced diet.

JUN 20221 | 23

REFLE Tin Wei Won
CTION 284860

Through this project, I have known that linear algebra
can be used in many aspects of our daily life such as
budgeting, making schedule, shopping and so on. It can
be no solution, unique solution or many solutions when
solving the linear equation. Sometimes, we need to have
exactly one solution to make our life easier or many
solutions to have more possibilities. Besides that, it also
is a new experience for me to do a mathematics project
in a form of magazine. It provides a good chance to

enrich our creativity and imagination.



24 | JUN 2022

REFLE Foo Jia En
CTION 284885

In this project, I learned more about the system of linear
equations and investigated its practical use in our daily lives. We

conducted extensive research and studied a lot of references to
verify that the information and data we wrote was accurate. For

example, I have studied the average calories consumed by a
person to ensure the data we input in the system of the linear
equation we created are realistic.In addition, I understand that
there were several types of system of linear equations such as no
solution, many solutions and exactly unique solutions. During
processing this project, the concept of the system may be easier to
comprehend if we apply and relate them to our daily situations.
Such as relating them when we are buying donuts, crossing a
road and even doing a chemistry experiment. By understanding
the concept and practising it in our life at the same time could
really help us to solve many problems. Moreover, I have used my
skills to complete the system linear equation by using Microsoft
Excel while working on this project. I have learned a lot of things
and successfully used the knowledge we have to overcome all the

difficulties we faced during this project.

JUN 20221 | 25

REFLE Lee Xue Lin
CTION 285888

By accomplishing this project, I have gained extensive
knowledge of how linear equations operate and the

beauty of linear equations. Before starting this project,
we had studied many references to ensure that we had

enough knowledge and also information to solve the
linear equation appropriately. During this period, I
have also found that linear equations are used a lot in
our daily lives. They might be exactly one solution,
infinitely many solutions, or no solution. Many of
them will give us exactly one solution. However, there

are cases when we will also have infinitely many
solutions or even no solution. In addition, we learned to

persevere when solving linear equations, despite the
numerous challenges we faced at the time.

26 | JUN 2022

REFLE Ooi Xin Yee
CTION 286871

To finish this project, I did research on topics about
systems of linear equations and made a group
discussion among group members to execute this

assignment without making any major errors. Through
this group project, I have learned that linear equations
can be applied in a variety of situations in our daily
lives. Such as, planning for a budget, calculating the

rates and making cost predictions. What was
challenging to me was the calculation which needed to
be calculated precisely. This assignment was enjoyable
for me because it has taught me the fundamentals of

linear equations.

JUN 20221 | 27

Reference

1. HISTORY OF UUM. (2018, April 25). Phppiuum.

https://phppiuum.wixsite.com/phppiuum/post/all-

about-uum

2. Gauss-Jordan Method - an overview | ScienceDirect

Topics. Retrieved June 17, 2022, from

https://www.sciencedirect.com/topics/mathematics/g

auss-jordan-method#:~:text=The%20Gauss-

Jordan%20method%20is,each%20pivot%20are%20ze

roed%20out.&text=After%20performing%20Gaussian

%20elimination%20on,in%20reduced%20row%20ech

elon%20form

3. Karen Gardner. “Recommended Calorie Intake for

One Meal.” LIVESTRONG.COM, 25 July 2019,

www.livestrong.com/article/440135-recommended-

calorie-intake-for-one-meal/.

4. S. (2016b, June 1). History of Universiti Utara

Malaysia (UUM). SyahirahTemezeBlog.

https://syahirahtemezeblog.wordpress.com/2016/05/

20/history-of-universiti-utara-malaysia-uum/

JUN 2022 | 28

Reference

5. Wikipedia contributors. (n.d.). Universiti Utara
Malaysia. Wikipedia. Retrieved June 18, 2022, from
https://en.wikipedia.org/wiki/Universiti_Utara_MalaysiaS.
(2016, June 1). History of Universiti Utara Malaysia
(UUM).

JUN 2022 | 29

Apenddix

Solution in Excel

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Apenddix

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Apenddix

GOOGLE FORM
Responden 1 (Siti)

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Apenddix

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Apenddix

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Apenddix

Respondent 2 (Mei Ling)

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Apenddix

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Apenddix

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Apenddix

Respondent 3 (Ali)

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Apenddix

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Apenddix

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Apenddix

Respondent 4 (Mutu)

JUN 2022 | 41

Apenddix

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Apenddix

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Published by 3K UUM