Free Printable Solving Problems Involving Linear Equations in Two Variables

1.

Which system of equations has a graph that shows intersecting lines with (3, −1) as a solution?

a)

a.

b)

b.

c)

c.

d)

d.

2.

Which of the following is a solution to the the system 3x+2y=7 and x-5y=8?

a)

(1, 3)

b)

(3, 1)

c)

(-1, 3)

d)

(3, -1)

3.

What is the solution of 𝑥 – 𝑦 = 4 and 𝑥 = 2𝑦 if substitution is applied?

a)

(8, 4)

b)

(4, 8)

c)

(-8, 4)

d)

(-4, 8)

4.

What is the solution or solution set of the system of linear equations given by 2𝑥 – 6𝑦 = 4 and 𝑥 = 3𝑦 + 4 when solved using substitution?

a)

(1, 0)

b)

(2, 0)

c)

no solution

d)

infinitely many solutions

5.

Which of the following ordered pairs does not satisfy both 2𝑥 – 4𝑦 – 8 = 0 and 𝑥 = 2𝑦 + 4 if substitution is applied?

a)

(0, -2)

b)

(4, 0)

c)

(-2, 3)

d)

(2, -1)

6.

What expressions should be multiplied to the system of linear equations 2𝑥 + 4𝑦 = 8 and 𝑥 – 𝑦 = 4 to eliminate first a variable y?

a)

2

b)

4

c)

6

d)

8

7.

What is the solution to the systems 𝑥 + 2𝑦 = 2 and 𝑥 – 2𝑦 = 2 when solved using elimination method?

a)

(0, 2)

b)

(0, -2)

c)

(2, 0)

d)

(-2, 0)

8.

Which of the following is a solution to the system of linear equations 𝑥 – 𝑦 = 4 and 2𝑥 + 2𝑦 = 8 when solved using elimination method?

a)

(0, 4)

b)

(4, 0)

c)

(0, -4)

d)

-4, 0)

9.

Elena went to a fast food restaurant. Four cheeseburgers and 2 large cokes cost a total of Php 118.00. Two large cokes cost Php 3.00 more than one cheeseburger. Let it be x for the cost of cheeseburger and y for the cost of a large coke. What mathematical equations can we get from the statement?

a)

a.

b)

b.

c)

c.

d)

d.

10.

Elena went to a fast food restaurant. Four cheeseburgers and 2 large cokes cost a total of Php 118.00. Two large cokes cost Php 3.00 more than one cheeseburger. Let it be x for the cost of cheeseburger and y for the cost of a large coke. What is the cost of a cheeseburger?

a)

Php 13.00

b)

Php 23.00

c)

Php 33.00

d)

Php 43.00

11.

Elena went to a fast food restaurant. Four cheeseburgers and 2 large cokes cost a total of Php 118.00. Two large cokes cost Php 3.00 more than one cheeseburger. Let it be x for the cost of cheeseburger and y for the cost of a large coke. What is the cost of a large coke?

a)

Php 13.00

b)

Php 23.00

c)

Php 33.00

d)

Php 43.00

12.

Mang Allan gave money to his daughters Lalai (x) and Bebe (y) for their school’s allowance. Both of his daughters received a total of 10 pieces of P10 coins. Bebe who needs more money for her project had received 2 pieces more than that of her sister Lalai. How many pieces of P10 coins did Lalai receive?

a)

2

b)

4

c)

6

d)

8

13.

Mang Allan gave money to his daughters Lalai (x) and Bebe (y) for their school’s allowance. Both of his daughters received a total of 10 pieces of P10 coins. Bebe who needs more money for her project had received 2 pieces more than that of her sister Lalai. How many pieces of P10 coins did Bebe receive?

a)

2

b)

4

c)

6

d)

8

14.

Mang Allan gave money to his daughters Lalai (x) and Bebe (y) for their school’s allowance. Both of his daughters received a total of 10 pieces of P10 coins. Bebe who needs more money for her project had received 2 pieces more than that of her sister Lalai. Which of these graphs shows the relationships of their allowances?

a)

b)

c)

d)

15.

The following systems of equations show coincident lines with infinitely many solutions. Which of these has some solutions such as (−1, 13), (0, 10), (1, 7) and (2, 4)?

a)

a.

b)

b.

c)

c.

d)

d.

16.

Which of the following are written in standard form?

a)

y=3x-5

b)

3x+16=5y

c)

2/3 x + 9/13 y = 21

d)

5x+7y=-12

17.

Which equation is written in STANDARD form?

a)

y = 1/2x + 2

b)

y - 3 = -5(x + 2)

c)

-7x + 2y = 9

d)

3x + 2 = y

18.

What is the definition of a variable?

a)

The letter used to represent a quantity

b)

The little number or letter used to raise to a power

c)

The number in front of a variable

d)

The number with no variable

19.

The graph of ax + by + c = 0 is _____

a)

A straight line parallel to x - axis

b)

A straight line parallel to y - axis

c)

A general straight line

d)

A line in the 2nd and 3rd quadrant

20.

In slope intercept form (y=mx+b) what is the "m"?

a)

The y-intercept

b)

The x-intercept

c)

The slope (rate of change)

d)

A point

21.

What is the y-intercept in the equation?
y = 5x - 4

a)

5

b)

-4

c)

-5

d)

4

22.

Write an equation in Standard Form.
A store sells t-shirts for $12 each and sweatshirts for $15 each. You plan to spend $120 on t-shirts and sweatshirts.

a)

2x + 5y = 120

b)

12x + 15y = 120

c)

12 + 15y = 2x

d)

12x + 15 = 120

23.

x + 20 = 100

a)

x = 80

b)

x = -5

c)

x = 20

d)

x = -80

24.

Solve for x:

a)

x = 20

b)

x = 7

c)

x = 10

d)

x = 3

25.

What does the "b" stand for in y=mx+b?

a)

slope

b)

x-intercept

c)

y-intercept

d)

constant

26.

Variables of linear equation is implicitly raised to

a)

second power

b)

four power

c)

third power

d)

first power

27.

Example of linear equation involving two variables is

a)

7a+8b+9c = 10+5

b)

8x = 2+10

c)

7x+3y+4z = 20

d)

6x+2y = 10

28.

In linear equation 'ax+by = c' a,b and c are considered as

a)

zero

b)

real numbers

c)

constants

d)

variable

29.

The geometrical representation of a linear equation

a)

Straight line

b)

Curve

c)

Parabola

d)

Either (b) or (c)

30.

Which of the following expressions is a linear expression in one variable?

a)

x²+ 1

b)

x + 2y

c)

x³

d)

7x + 5

31.

To be identified as a Linear Equation, what must be the highest exponential degree of its variable?

a)

0

b)

1

c)

2

d)

None

32.

What is pair of linear equations in two variables?

a)

a set of two or more linear equations in the same two variables

b)

a polynomial with three terms

c)

set of two linear equations in same two variables

33.

How many variables should be present in the given linear equation in able to consider as an example of Linear Equation in Two Variables?

a)

Four Different Variables

b)

Two Identical Variables

c)

Four Identical Variables

d)

Two Different Variables

34.

2x+3y=5 is wriiten in what form?

a)

Standard Form

b)

Slope-intercept Form

35.

y = -4x + 7 is written in what form?

a)

Standard Form

b)

Slope-intercept Form

36.

Which of the following is an example of Linear equation in Two Variables?

a)

x²- 25

b)

a³ - 27

c)

4x = 2y - 9

d)

x² + 3x + 2

37.

Fifteen more than three times a number is the same as ten less than six times the number. What is the number ?

a)

15/3

b)

25/3

c)

25

d)

40

38.

The sum of three consecutive integers is 93. What is the value of the second integer?

a)

31

b)

34

c)

36

d)

38

39.

Find the three consecutive odd integers so that the sum of twice the first, the second and three times the third is 152.

a)

15,17,19

b)

19,21, 23

c)

23, 25, 27

d)

27, 29, 31

40.

A man is 41 years old and in seven years he will be four times as old as his son is at that time. How old is his son now?

a)

5

b)

7

c)

9

d)

10

41.

Peter’s age 13 years ago was 1/3 of his age 7 years hence. How old is peter?

a)

10

b)

13

c)

15

d)

23

42.

A motorboat goes downstream in river and covers a distance between two coastal towns in 5 hours. It covers this distance upstream in 6 hours. If the speed of the stream is 3 km/hr, find the speed of the boat in still water.

a)

30km/h

b)

33km/h

c)

35km/h

d)

37km/h

43.

A sofa and a love seat together costs ₱21,750. The sofa costs double the love seat. How much is the cost of love seat?

a)

₱7,500

b)

.₱7,100

c)

₱7,150

d)

₱7,250

44.

9.) A total of ₱100,000 is distributed among 150 persons as gift. A gift is either of ₱ 500 or ₱ 1000. How many ₱ 500 worth of gifts are distributed?

a)

25

b)

50

c)

75

d)

100

45.

The length of a rectangle is twice its width. If the perimeter is 72 metre, find the length of the rectangle.

a)

12m.

b)

18m

c)

24m

d)

26m

46.

If 28 less than five times a certain number is 232. What is the number?

a)

260

b)

204

c)

140

d)

52

47.

Fifteen more than three times a number is the same as ten less than six times the number. What is the number ?

a)

15/3

b)

25/3

c)

25

d)

40

48.

The sum of three consecutive integers is 93. What is the value of the second integer?

a)

31

b)

34

c)

36

d)

38

49.

Find the three consecutive odd integers so that the sum of twice the first, the second and three times the third is 152.

a)

15,17,19

b)

19,21, 23

c)

23, 25, 27

d)

27, 29, 31

50.

A man is 41 years old and in seven years he will be four times as old as his son is at that time. How old is his son now?

a)

5

b)

7

c)

9

d)

10

51.

Peter’s age 13 years ago was 1/3 of his age 7 years hence. How old is peter?

a)

10

b)

13

c)

15

d)

23

52.

A motorboat goes downstream in river and covers a distance between two coastal towns in 5 hours. It covers this distance upstream in 6 hours. If the speed of the stream is 3 km/hr, find the speed of the boat in still water.

a)

30km/h

b)

33km/h

c)

35km/h

d)

37km/h

53.

A sofa and a love seat together costs ₱21,750. The sofa costs double the love seat. How much is the cost of love seat?

a)

₱7,500

b)

.₱7,100

c)

₱7,150

d)

₱7,250

54.

9.) A total of ₱100,000 is distributed among 150 persons as gift. A gift is either of ₱ 500 or ₱ 1000. How many ₱ 500 worth of gifts are distributed?

a)

25

b)

50

c)

75

d)

100

55.

The length of a rectangle is twice its width. If the perimeter is 72 metre, find the length of the rectangle.

a)

12m.

b)

18m

c)

24m

d)

26m

56.

If 28 less than five times a certain number is 232. What is the number?

a)

260

b)

204

c)

140

d)

52

57.

The standard form of a linear equation in two variables is ____________.

a)

y = mx + b

b)

x + y = m

c)

Ax + By = C

d)

By = Ax + C

58.

Find the value of A in the linear equation in two variable 4x + 2y = 8

a)

8

b)

4

c)

2

d)

16

59.

In the equation 7x - y = 2, What is the value of B?

a)

2

b)

5

c)

-1

d)

7

60.

Find the value of C in the equation x + 3y = -10

a)

-10

b)

3

c)

13

d)

1

61.

The graph of a linear equation in two variables form a ___________.

a)

parabola

b)

circle

c)

rectangle

d)

line

62.

(2,-3) is a solution to the equation 3x - 4y = 18

a)

False

b)

True

63.

Which of the following is a solution to the equation 4x - y = -5?

a)

(-5,1)

b)

(-2,-3)

c)

(1,-2)

d)

(-1,10)

64.

Give the values of A, B & C respectively, in the equation 8y + 12 = -4x when written in standard form.

a)

A=8, B =-4 & C=12

b)

A=4, B = 12 & C=-8

c)

A=-12, B = 8 & C=4

d)

A=4, B =8 & C=-12

65.

A linear equation in two variables has infinitely many solutions.

a)

True

b)

False

66.

Write the equation 5x = 3y - 15 in Standard Form.

a)

3y = -5x + 15

b)

5x + 15 = 3y

c)

$y=\frac{5}{3}x\ +\ 5$

d)

5x - 3y = -15

67.

The standard form of a linear equation in two variables is ____________.

a)

y = mx + b

b)

x + y = m

c)

Ax + By = C

d)

By = Ax + C

68.

Find the value of A in the linear equation in two variable 4x + 2y = 8

a)

8

b)

4

c)

2

d)

16

69.

In the equation 7x - y = 2, What is the value of B?

a)

2

b)

5

c)

-1

d)

7

70.

Find the value of C in the equation x + 3y = -10

a)

-10

b)

3

c)

13

d)

1

71.

The graph of a linear equation in two variables form a ___________.

a)

parabola

b)

circle

c)

rectangle

d)

line

72.

(2,-3) is a solution to the equation 3x - 4y = 18

a)

False

b)

True

73.

Which of the following is a solution to the equation 4x - y = -5?

a)

(-5,1)

b)

(-2,-3)

c)

(1,-2)

d)

(-1,10)

74.

Give the values of A, B & C respectively, in the equation 8y + 12 = -4x when written in standard form.

a)

A=8, B =-4 & C=12

b)

A=4, B = 12 & C=-8

c)

A=-12, B = 8 & C=4

d)

A=4, B =8 & C=-12

75.

A linear equation in two variables has infinitely many solutions.

a)

True

b)

False

76.

Write the equation 5x = 3y - 15 in Standard Form.

a)

3y = -5x + 15

b)

5x + 15 = 3y

c)

$y=\frac{5}{3}x\ +\ 5$

d)

5x - 3y = -15

77.

Which of the following functions should be used to solve problems involving a constant rate of change?

a)

exponential function

b)

linear function

c)

polynomial function

d)

quadratic function

78.

Which of the following is the standard form of a linear function?

a)

f(x) = bx + m

b)

f(x) = bx - m

c)

f(x) = mx + b

d)

f(x) = mx - b

79.

Mr. Nilo, a mathematics teacher, charges Php200 per hour for tutorial service to a junior high school student. If he spends 3 hours tutoring per day, how much would he receive in 12 days?

a)

. Php 6,300

b)

Php 7,200

c)

Php 7,300

d)

Php 8,100

80.

Beverly’s car uses 15 liters of gasoline to travel 120 kilometers. At that rate, how many liters of gasoline will her car consume to travel 130 kilometers?

a)

15.25 liters

b)

16.25 liters

c)

17.25 liters

d)

18.25 liters

81.

Joshua likes to read a magazine. He reads 50 pages in 2 hours. At the same rate, how many hours will it take him to read the remaining 150 pages?

a)

6

b)

7

c)

8

d)

9

82.

Lyoid works as a service crew in a fast food center where he earns Php82.00 per hour. How much will he earned in a day if he works 8 hours straight?

a)

Php 556

b)

Php 656

c)

Php 756

d)

Php 856

83.

Lyoid works as a service crew in a fast food center where he earns Php82.00 per hour. How much will Lyoid earn in 3 days?

a)

Php 1,668

b)

Php 1,968

c)

Php 2,268

d)

Php 2,568

84.

Queenie is working in a restaurant and her hourly wage is Php51.68. Let x represents the number of hours worked and let f(x) represents the total amount earned. Which of the following functions best represents the total amount earned by day?

a)

f(x) = 51.68x

b)

f(x) = x + 51.68

c)

f(x) = x - 51.68

d)

f(x) = 51.68 - x

85.

Queenie is working in a restaurant and her hourly wage is Php51.68. Let represents the number of hours worked and let f(x) represents the total amount earned, if Queenie works 8 hours a day, how much will she earn in 14 days?

a)

Php 4,778.16

b)

Php 4,878.16

c)

Php 5,788.16

d)

Php 5,878.16

86.

JC works as a salesman in a company that distributes top brands and latest model of cellular phones. He receives a commission of Php1,500 for every cellular phone unit he sells. On top of the commission, he receives a monthly salary of Php12,000. What is his commission if he sells 25 cellphones in a month?

a)

Php 27,000

b)

Php 37,500

c)

Php 46,500

d)

Php 47,500

87.

JC works as a salesman in a company that distributes top brands and latest model of cellular phones. He receives a commission of Php1,500 for every cellular phone unit he sells. On top of the commission, he receives a monthly salary of Php12,000. How many cellphones should he sell in a month to make an income of Php79,500?

a)

45

b)

58

c)

65

d)

67

88.

Al John spent Php1,200 on N95 facemasks because of pandemic. Each facemask costs Php100. How many facemasks did he buy?

a)

10

b)

12

c)

15

d)

95

89.

Jun Mark used 15 m of copper wire which weighs 1 kg. If a copper wire weighs 3.5 kg, how many meters is it?

a)

50 m

b)

52.5 m

c)

53.5 m

d)

54 m

90.

Ranie worked in the store for 5 hours. He earned a total of Php1,500. How much does he earn each hour?

a)

Php 300

b)

Php 400

c)

Php 500

d)

Php 600

91.

.Puto balanghoy or steamed cassava cake is traditionally made in the Visayas region using basic ingredients such as cassava, brown sugar and grated coconut. Marvin is selling a puto balanghoy in the function of f(x) = 10x, how much is Marvin’s income if a customer wants to buy a total of 50 pieces?

a)

Php 450

b)

Php 500

c)

Php 550

d)

Php 600

Solving Problems Involving Linear Equations in Two Variables

Total questions: 91

Worksheet time: 1hrs 24mins

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