Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics. It is typically taught to secondary school students and builds on their understanding of arithmetic.

1. Elementary
Algebra
Fatima S. Lara and Anafel F. Into

2. Table of Contents
Linear Equation
Real Numbers
Linear Equation in
Two Variable

3. Real Numbers
Easy

4. The type of number we normally use, such as 1, 15.82,
−0.1, 3/4, etc.
Positive or negative, large or small, whole numbers or
decimal numbers are all Real Numbers.
They are called "Real Numbers" because they are not
Imaginary Numbers.
What is a
Real Numer?

5. Properties of Real Numbers

6. Properties of Real Numbers

7. Word Problems
involving Real
Numbers
Ana has a negative balance of
600php in his bank account. If
she deposit 3550php into her
account. How much money does
Ana have in her account after
the deposit?
1. What is the problem?
How much Ana have in her account
after the deposit?
Problem 1:
Steps in Problem
Solving:
2. What is given?
Negative 600php and deposit
3550php

8. 3. What is the solution?
-600php + 3,550php = ?
5. Checking
Therefore, Ana have 2,950php in
her account.
4. Solving the Problem
-600php + 3,550php =
2,950php

9. In Baguio City, Philippines the
temperature was -14 °F in the
morning. If the temperature
dropped 7°F, what is the
temperature now?
1. What is the problem?
What is the present temperature?
Problem 2: Steps in Problem
Solving:
2. What is given?
-14°F and -7°F

10. 3. What is the solution?
-14°F + -7°F = ?
5. Checking
Therefore, the temperature now is
-21°F.
4. Solving the Problem
-14°F + -7°F = -21°F

11. A submarine at -38feet
dives 50feet. What is the
submarine elevation after the
dive?
1. What is the problem?
What is the submarine elevation
after the dive?
Problem 3: Steps in Problem
Solving:
2. What is given?
-38feet and -50feet

12. 3. What is the solution?
-38feet + -50feet = ?
5. Checking
Therefore, the submarine elevation
after the dive is -88feet.
4. Solving the Problem
-38feet + -50feet = -88feet

13. Submarine was situated
800feet below sea level. If it
ascends 250feet. What is the
new position?
1. What is the problem?
What is the new position of the
submarine situated?
Problem 4: Steps in Problem
Solving:
2. What is given?
-800feet and 250feet

14. 3. What is the solution?
800feet + 250feet =?
5. Checking
-800feet + 250feet = -550feet
4. Solving the Problem
-800feet + 250feet = -550feet

15. The Jurassic period was
believed to have started about
190,000,000 B.C. and ended
about 135,000,000 B.C. About
how long was this?
1. What is the problem?
How long Jurassic period last?
Problem 5: Steps in Problem
Solving:
2. What is given?
190,000,000 B.C. and 135,000,000
B.C.

16. 3. What is the solution?
190,000,000 B.C – 135,000,00
B.C. =?
5. Checking
Therefore, the Jurassic period last for
about 55,000,000 B.C.
4. Solving the Problem
190,000,000 B.C – 135,000,00
B.C. = 55,000,000 B.C.

17. Problem Solving involving
Linear Equation
Average

18. Linear Equation
*Linear equations are equations of the first
order. These equations are defined for lines in
the coordinate system. An equation for a
straight line is called a linear equation. The
general representation of the straight-line
equation is y=mx+b, where m is the slope of the
line and b is the y-intercept.
Linear equations are those equations that are of
the first order. These equations are defined for
lines in the coordinate system.

19. Linear Equation

20. Slope - Intercept

21. 01
1. Ana created an instagram account and started with 3 following (her mom, her dad, and her
sister). She plans to find 7 new followers each day. Create an equation that describes how
many followers she has each day. How many followers will she have after 10days? 100 days?
Steps in Problem Solving:
1. What is the problem?
How much follower she have after 10days?
100days?
2. What is given?
3followers, 7followers, 10days and 100days
3. What is the solution?
y = mx + b
y = 7x + 3
4. Solving the Problem
y = mx + b
y = 7x + 3
x = 10 x = 100
y = 7(100) + 3
y = 7(10) + 3 y = 700 + 3
y = 70 + 3 y = 703
y = 73
5. Checking
Therefore, after 10days Ana has 73 followers.
Therefore, after 100days Ana has 703 followers.

22. 02
1. Mr. Lam wants to create a library of books in his classroom. He is starting with 12 books.
He plans to buy 3 new books each week. Create an equation that describe the number of
books Mr. Lam has each week. How many books does Mr. Lam have after 5 weeks? 10
weeks?
Steps in Problem Solving:
1. What is the problem?
How many books does Mr. Lam have after 5 weeks? 10
weeks?
2. What is given?
3 new books, 12 books, after 5weeks and after 10 weeks
3. What is the solution?
y = mx + b
y = 3x + 12
4. Solving the Problem
y = 3x + 12
x = 5 x = 10
y = 3(5) + 12 y = 3(10) + 12
y = 15 + 12 y = 30 + 12
y = 27 y = 42
5. Checking
Therefore, after 5 weeks Mr. Lam has 27
books.
Therefore, after 10 weeks Mr. Lam has 42
books.

23. 03
Ms. Ruddy opens a retirement account and the starting is 3000php. She plans to add
1000php per month to the account. Make an equation that describes the amount of money in
the account each month. How much money does Ms. Ruddy have after 6 months? 12
months?
Steps in Problem Solving:
1. What is the problem?
How much money does Ms. Ruddy have after 6 months? 12 months?
2. What is given?
Starting is 3000php, 1000php per month, 6 months and 12 months.
3. What is the solution?
y = mx + b
y = 1000phpx + 3000php

24. 4. Solving the Problem
y = 1,000phpx + 3000
x = 6 x = 12
y = 1,000php (6) + 3000php y = 1,000php (12) + 3000php
y = 6000php + 3000php y = 12,000php + 3000php
y = 9000php y = 15,000php
5. Checking
Therefore, after 6 months Ms. Rudy has 9000php.
Therefore, after 12 months Ms. Rudy has 15,000php.

25. 04
Mira wants to gain weight. She started with 45kg. Her goal is to gain 3kg every week. Make
an equation that describes the weight Mira gain every week. How much weight does Mira gain
after 2 months?
5 months?
Steps in Problem Solving:
What is the problem?
How much weight does Mira gain after 2 months? 5 months?
What is given?
45kg, 3kg every week, 2 months and 5 months
What is the solution?
y = mx + b
y = 3kg x + 45kg

26. Solving the Problem
x = 2 x = 5
y = 3kg (2) + 45kg y = 3kg (5) + 45kg
y = 6kg + 45kg y = 15kg + 45kg
y = 51kg y = 60kg
Checking
Therefore, after 2 months Mira gain 51kg.
Therefore, after 5 months Mira gain 60kg.

27. 05
Ben opens a store. The starting capital is 50,000php. He plans to add 10,000 each month. Create
and equation that describes the amount Ben added each month for his store. How much does Ben
have added after 1 year? 2 years?
Steps in Problem Solving:
1. What is the problem?
How much does Ben have added after 1 year? 2 years?
2. What is given?
Capital 50,000php, 10,0000php per month, 12 months and 24 months.
3. What is the solution?
y = mx + b
y = 10,000phx + 50,000php

28. 4. Solving the Problem
y = 10,000php + 50,000php
x = 12
y = 10,000php (12) + 50,000php
y = 120,000php + 50,000php
y = 170,000php
x = 24
y = 10,000phpx + 50,000php
y = 10,000php (24) + 50,000php
y = 240,000php + 50,000php
y = 290,000php
5. Checking
Therefore, after 12 months Ben has added 170,000php.
Therefore, after 24 months Ben has added 290,000php

29. Linear Equation in
Two Variables using
Elimination and
Substitution.

30. What is Linear Equation in
Two Variables?

31. What are the methods in Solving
Linear Equation involving Two
Variables?
1. Substitution
2. Elimination
3. Graphing
4. Matrix

38. What is a Linear Equation in two variables?
A linear system of two equations with two
variables is any system that can be written in the
form.
ax + by = p
cx + dy = q
A solution to a system of equations is a value of x
and a value of y that, when substituted into
the equations, satisfies both equations at the same
time.

39. There are x chairs and y tables
in a room. There are 8 chairs
and tables in all. The number of
tables is 2 less than the number
of chairs. How many chairs and
tables are there?
1. What is the problem?
How many chairs and tables in the
room ?
Problem 1 : Steps in Problem
Solving:
2. What is given?
x = the no. of chairs
y = the no. of tables
8 chairs and tables in all

40. 3. What is the solution?
y = x - 2 -x + y = -2
x + y = 8
Solution using Elimination Method
x + y =8
+ -x + y =-2
2y = 6
2y/2 = 6/2
y = 3 no. of tables
Substitute y = 3
x + y = 8
x + 3 = 8
x = 8 – 3
x = 5 no. of chairs
5. Checking
Therefore, there are 5 chairs and 3
tables in the room.
4. Solving the Problem
Solution using Substitution Method
y = x - 2 -x + y = -2
x + y = 8
x + (x-2) = 8
2x - 2 = 8
2x = 8 + 2
2x = 10
2x/2 = 10/2
x = 5 no. of chairs
y = x – 2
y = 5 – 2
y = 3 no. of tables

41. Your teacher is giving you a test
worth 100 points containing 40
questions. There are two –
points and four - points
questions on the test. How many
of each types of question are on
the test?
1. What is the problem?
How is the total two - points and
four – points question on the test ?
Problem 2 : Steps in Problem
Solving :
2. What is given?
x = total questions of two - points
y = total questions of four – points
100 points and 40 questions

42. 3. What is the solution?
x + y = 40
2x + 4y = 100
Solution using Elimination Method
x + y = 40 -2(x + y = 40)
+ 2x + 4y = 100 + 2x + 4y = 100
-2x + 2y = -80
+ 2x + 4y = 100
2y = 20
2y/2 = 20/2
y = 10 total questions of 4 points
Substitute y = 10
x + y = 40
x + 10= 40
x = 40 – 10
x = 30 total questions of 2 points
5. Checking
Therefore, there are 30 questions of 2
points and 10 questions of 4 points on
the test.
4. Solving the Problem
Solution using Substitution Method
x + y = 40 y = 10 x + y = 40
2x + 4y = 100 x + 10 = 40
2( 40 – y ) + 4y = 100 x = 40 - 10
80 – 2y + 4y = 100 x = 30 total
80 + 2y = 100 questions
2y = 100 – 80 of 2 points
2y = 20
2y/2 =20/2
y = 10 total questions of 4 points

43. There are 25 students in a room.
The number of females students
is 9 more than the number of
male students. How many
female students are there? Male
students?
1. What is the problem?
How many female and male
students are there in the room?
Problem 3 : Steps in Problem
Solving :
2. What is given?
x = the number of male students
y = the number of female students
25 students in the room

44. 3. What is the solution?
x + y = 25
y = x + 9
Solution using Elimination Method
x + y = 25 x + y =25
y = x + 9 - x + y = 9
2y = 34
2y/2 = 34/2
y = 17 total
number of female students
Substitute y = 17
x + y = 25
x + 17 = 25
x = 25 – 17
x= 8 total number of male students
5. Checking
Therefore, there are 17 female and 8
male students in the room.
4. Solving the Problem
Solution using Substitution Method
x + y = 25 substitute: y = x + 9
y = x + 9 y = 8 + 9
x + y = 25 y = 17 total
x + (x + 9) = 25 number of
2x + 9 = 25 females
2x = 25 – 9 students
2x = 16
2x/2 = 16/2
x = 8 total number of male students

45. Roman’s age is three times the
sum of the ages of his tow son’s.
After 5 years his age will be
twice the sum of the ages of his
two son’s. Find the age of
Roman?
1. What is the problem?
What is the age of Roman?
Problem 4: Steps in Problem
Solving :
2. What is given?
x = Roman’s age 3times
y = the sum of ages of his two son’s
5 + 5 , y+10
After 5 years = x + 5

46. 3. What is the solution?
x + 5 = 2 (y + 10)
x = 3y
Solution using Elimination Method
x + 5 = 2 ( y + 10) = x – 2y = 15
x = 3y = + -x + 3y = 0
y = 15 son’s age
Substitute y = 15
x = 3y
x= 3 (15)
x= 45 Roman’s age
5. Checking
Therefore, Roman’s age is 45years old.
4. Solving the Problem
Solution using Substitution Method
x + 5 = 2( y + 10)
x + 5 = 2y + 20
x - 2y = 20 – 5
x – 2y = 15
Substitute x = 3y
3y – 2y = 15
y = 15 son’s ages
Substitute y = 15
x = 3 ( 15)
x = 45 Roman’s age

47. Michael and Tom are brothers.
Their combined age is 20 and
Tom is 4 years older than
Michael. What are Michael and
Tom’s ages?
1. What is the problem?
What are Michael and Tom’s ages?
Problem 5: Steps in Problem
Solving :
2. What is given?
x = Michael’s age
y = Tom’s age is 4times older
The combined ages is 20.

48. 3. What is the solution?
x + y = 20
y = x + 4
Solution using Elimination Method
x + y = 20 x + y = 20
y = x + 4 + -x + y = 4
2y = 24
2y/2 = 24/2
y = 12 Tom’s age
Substitute y = 12
y = x + 4
12 = x + 4
12-4 = x
x = 8 Michael’s age
5. Checking
Therefore, Michael’s age is 8 and Tom’s
age is 12.
4. Solving the Problem
Solution using Substitution Method
x + y = 20 x + y = 20
y = x + 4 8 + y = 20
x + (x + 4) = 20 y = 20 - 8
x + x + 4 = 20 y = 12 Tom’s age
2x + 4 = 20
2x = 20 – 4
2x = 16
2x/2 = 16/2
x = 8 Michael’s age

49. THANK YOU !!!

50. Elementary
Algebra
Fatima S. Lara and Anafel F. Into