ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​In this module, you will be able to:

 Illustrate linear equations in two variables.

M8AL- Ie-3

Specifically, you are expected to:

1. illustrate linear equations in two variables; and

2. determine if an ordered pair is a solution of a given linear equation.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​1. Translate this real – life situation into mathematical equation: Pamela bought 5 blouses (b) and 2 pants (p) at South Seas Mall. The total amount she paid for the items was Php 2000.

a. b + p = 2000

b. 2b + 5p = 2000

c. 5b + 2p = 2000

d. 5b + p = 2000

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​2. Which of the following real-life situations represents a linear equation in two variables?

​

a. The difference between twice a number and eight is 50.

b. The product of m and n is equal to 18.

c. The sum of the ages of Ryan and John is equal to 54.

d. The number added to eight is twenty.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​4. Which of the following is NOT an example of linear equation in two variables?

a. 3x – 5y = 2

b. y = -8x

c. 2xy + 8y = 10

d. 3(x + 2y) = 5

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​5. It is an ordered pair that makes the

given linear equation in two variables true.

a. coordinate

b. solution

c. point

d. slope

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​6. How many solution/s does/do a linear equation in two variables have?

​a. one

b. two

c. infinite

d. no solution

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​7. What is the graph of a linear equation in two variables?

​a. Parabola

b. Straight Line

c. Half – Plane

d. Half - Parabola

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​For item numbers 8 and 9, refer to the situation below:

​Jose, who is the SSG Business Manager, was given the task by the SSG President to canvass for a tarpaulin printing. He knew that in printing ad, the charge of tarpaulin printing is Php 12 per square foot and Php 100 for the lay outing.

​8. Which of the following equations best represents the total cost (y) with (x) number of square feet including lay outing fee?

a. y = 100x – 12

b. y = 100x + 12

c. y = 12x – 100

d. y = 12x + 100

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​For item numbers 8 and 9, refer to the situation below:

​Jose, who is the SSG Business Manager, was given the task by the SSG President to canvass for a tarpaulin printing. He knew that in printing ad, the charge of tarpaulin printing is Php 12 per square foot and Php 100 for the lay outing.

​9. The SSG President told Jose that the dimensions of the tarpaulin are 5 feet by 4 feet. How many square feet is the tarpaulin? How much should Jose pay for the printing ad?

a. 20 square feet; Php 420

b. 20 square feet; Php 340

c. 9 square feet; Php 320

d. 9 square feet; Php 208

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​10. Which of the following is a solution for the equation 2x – y = 8?

​a. (2, -4)

b. (2, 4)

c. (-2, -4)

d. (-2, 4)

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​11. Which of the following is NOT the solution for the equation 3x – 2y = 6?

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​12. As x increases in the equation 5x + y = 7, what happens to the value of y?

​a. increases

b. decreases

c. does not change

d. cannot be determined

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​13. In the equation 2x – 5y = -23, if x = -4, what is the value of y?

​a. 5

b. -5

c. 3

d. -3

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​14. In the equation, 3x – 4y = 25, if y = -1, what is the value of x?

​a. -4

b. 4

c. 7

d. -7

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​15. The perimeter of a rectangular pot is 332 cm. and the width is 76 cm. Find the length of the rectangular pot?

​a. 90 cm.

b. 256 cm.

c. 180 cm.

d. 128 cm.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 1: What’s Your Order?

Direction: Read the situation provided and answer the following questions below.

Food delivery services are very useful especially in this time of crisis due to COVID 19. Filipino families choose to order their foods online and be delivered in their respective homes with the help of Food Panda and other food delivery services. Food Panda charges a basic delivery fee of Php 50 and an additional Php 10 for each kilometer.

​Questions:

1. How much will you pay if your house is located 1 kilometer away from the store of purchase? What about for 2 kilometers? for 3 kilometers?

​__________________________________

​__________________________________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 1: What’s Your Order?

Direction: Read the situation provided and answer the following questions below.

Food delivery services are very useful especially in this time of crisis due to COVID 19. Filipino families choose to order their foods online and be delivered in their respective homes with the help of Food Panda and other food delivery services. Food Panda charges a basic delivery fee of Php 50 and an additional Php 10 for each kilometer.

​2. How far is the distance from your house to the store, for you to avail a delivery worth Php 100?

​__________________________________

​__________________________________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 2: Market Day

Direction: Read the situation provided and answer the following questions below.

Andi went to the public market to buy some fruits. She purchased mangoes with a total of 150 pesos from the fruit vendor but she needed to return mangoes and get banana and guavas instead. The fruit vendor said, “I will not refund you but you can get fruits equal to 150 pesos as an exchange”. The price of each guava is 12 pesos and the price of each banana is 5 pesos. How many pieces of banana and guava should she take to cover exactly the 150 pesos worth of mangoes?

​1. Were you able to answer the problem and help Andi to decide on how many pieces of banana and guava she is going to buy?

​__________________________________

​__________________________________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 2: Market Day

Direction: Read the situation provided and answer the following questions below.

Andi went to the public market to buy some fruits. She purchased mangoes with a total of 150 pesos from the fruit vendor but she needed to return mangoes and get banana and guavas instead. The fruit vendor said, “I will not refund you but you can get fruits equal to 150 pesos as an exchange”. The price of each guava is 12 pesos and the price of each banana is 5 pesos. How many pieces of banana and guava should she take to cover exactly the 150 pesos worth of mangoes?

​2. What mathematical equation represents the problem?

​__________________________________

​__________________________________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 2: Market Day

Direction: Read the situation provided and answer the following questions below.

Andi went to the public market to buy some fruits. She purchased mangoes with a total of 150 pesos from the fruit vendor but she needed to return mangoes and get banana and guavas instead. The fruit vendor said, “I will not refund you but you can get fruits equal to 150 pesos as an exchange”. The price of each guava is 12 pesos and the price of each banana is 5 pesos. How many pieces of banana and guava should she take to cover exactly the 150 pesos worth of mangoes?

​3. Think of at least 2 possible combinations that will satisfy the equation in number 2.

​__________________________________

​__________________________________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 3: Guide Me Through

Direction: Do what is asked. Write your answers on the space provided.

A. Determine whether the equation is a linear equation in two variables. If not, state the reason.

​_________

​_________

​_________

​_________

​_________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​B. Is the given ordered pair a solution to this equation 3x – 2y = -8?

​(4, 2) (-4, -2)

________ Write the equation ______________

__________ Substitute __________________

___________ Simplify ________________

__________ Does it make the equation TRUE? _________

___________ Solution or Not a solution? _____________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​To recall and sum up what you have learned from the lesson for today, answer the following questions below. Write your answer on the space provided.

​Activity 4: Solve, Then Decide!

Direction: Do what is asked. Write your answers on the space provided.

A. Write LE if the equation is linear, and NLE if it is not.

​___________

​___________

​___________

​___________

​___________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​B. Write S if the given ordered pair is a solution. Otherwise, write NS.

​1. y = 3x + 4 ; (2, 10)

2. 5x + 4y = 8; (4, –3)

3. 7x – 4y = 13; (3, 2)

​4. 2x – 3y = 8; (-3, -8)

5. x – 6y = 18; (0, -3)​

​________

​________

​________

​________

​________

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Activity 5: Money Matters

Direction: Read and analyze the following word problems. Show your complete solution on the space provided.

Abdul bought 5kg of rice and 3kg of fish. He paid a total amount of Php 440. If a kilo of fish is Php 80.00, how much does a kilo of rice cost?

Solution:

​_____________________________

​_____________________________

​_____________________________

​_____________________________

​_____________________________

​

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​Direction: Encircle the letter of the correct answer.

1. Translate this real – life situation into mathematical equation: The number of girls (g) in a class is five more than twice the number of boys (b).

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​2. Translate this real – life situation into mathematical equation: The sum of the ages of Cedric (c) and Justin (j) equals 50.

​a. c – j = 50

b. c + j = 50

c. 50 + c = j

d. 50 + j = c

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​3. Which of the following real – life situations represent a linear equation in two variables?

​a. Twice a number x yields 24.

b. The total of four times p and 3 is 19.

c. Three times the difference of x and y is 24.

d. Five times d squared added to q equals 30.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​4. Which of the following real – life situations does not represent a linear equation in two variables?

a. The sum of twice the number x and four times the number y is 36.

b. The number m added to twice the number n is 8.

c. The difference of the ages of Ryan and John equals 25.

d. The product of s and r divided by t.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​5. Which of the following is NOT a linear equation in two variables?

​a. 2x(x – 3y) = -5

b. 3(2x + 4y) = 24

c. 2x + 4y = 6

d. y = 5x - 3

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​For item numbers 6 and 7, refer to the situation below:

​Denise, who is the Class Treasurer, was given a task by the Class Adviser to canvass for a ceiling fan to be used in the classroom. With the help of her Mom who is also the HRPTA President, they found out that the least amount of ceiling fan with a good quality is Php 1150.00. A professional fee will also be needed for the installation of the ceiling fan which is worth Php 200.00.

​6. Which of the following equations best represents the total cost y with x number of ceiling fan including installation fee?

​a. y = 1150x + 200 c. y = 1150x + 200y

b. y = 200x + 1150y d. y = 200x + 1150

​

​

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​For item numbers 6 and 7, refer to the situation below:

​Denise, who is the Class Treasurer, was given a task by the Class Adviser to canvass for a ceiling fan to be used in the classroom. With the help of her Mom who is also the HRPTA President, they found out that the least amount of ceiling fan with a good quality is Php 1150.00. A professional fee will also be needed for the installation of the ceiling fan which is worth Php 200.00.

​7. Since Denise knew that their classroom needs two ceiling fans, how much should their class prepare for the said project?

a. Php 270.00 c. Php 2500.00

b. Php 250.00 d. Php 2700.00 ​

​

​

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​8. Is (-10, -12) a solution the equation -7x + 6y = 2?

​a. Yes

b. No

c. Maybe

d. Cannot be determined

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​9. Which of the following is a solution for the equation 3x – 4y = -3?

​a. (5, -3)

b. (-5, -3)

c. (-5, 3)

d. (5, 3)

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​10. Which of the following is NOT the solution for the equation 3x – 4y = -12?

​a. (-4, 0)

b. (-7, -4)

c. (4, 6)

d. (0, 3)

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​11. As y decreases in the equation x – 3y = -6, what happens to the value of y:

​a. increases

b. decreases

c. does not change

d. cannot be determined

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​12. In the equation 3x – 2y = 3, if x = -9, what is the value of y?

​a. 15

b. -15

c. -12

d. 12

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​13. In the equation, 5x + 4y = -8, if y = 3, what is the value of x?

​

​a. -4

b. 4

c. 7

d. -7

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​14. Andre needs to buy notebooks and pens for the opening of the school year. He has a total budget of Php 100.00, and each notebook costs Php 14.00 and each pen costs Php 8.00. If he buys 6 notebooks, how many pens can he buy?

​a. 1

b. 2

c. 3

d. 4

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​15. The perimeter of a rectangular pool is 1,032 inches and the length is 327 inches. Find the width of the rectangular pot?

​a. 378 in

b. 256 in

c. 352 in

d. 189 in

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

​This is another activity that you will surely enjoy while you enrich the knowledge and skill that you have learned in this lesson.

Direction: Analyze the problem below, and answer the questions that follow.

Problem:

At a sari – sari store, you notice that you can buy a biscuit for Php 6.00 and a candy for Php 1.00. You have a total of Php 42.00 to spend. You are feeling generous and want to share some snacks for your friends.

​A. Write an equation in standard form to present the number of biscuits (b), and the number of candies (c), that you can buy with Php 35.00.

ILLUSTRATE LINEAR EQUATION IN TWO VARIABLES

JUN DESCARGAR

B. Find five possible solutions to the linear equation from part (a), and plot the points on a Cartesian Plane.