Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

Use the following information to answer the next question.

A construction company pays its workers Rs 200 per day for working 6 hours. If a worker works overtime, he is paid an extra Rs 40 for every hour.

If a worker works for x extra hours in a day and his wage is y per day, then which equation is consistent with the given information?

A
x = 200 + 40y

B
x = 40 + 200y

C
y = 200 + 40x

D
y = 40 + 200x

Solution

Wage for working 6 hours a day = Rs 200

Overtime for working 1 extra hour = Rs 40

Hence, amount of money paid for working x extra hours = Rs 40x

Therefore, if y is the wage per day, then y = 200 + 40x

Thus, the required equation is y = 200 + 40x.

The correct answer is C.
Question 2
1 / -0

Point (3, 2) lies on the line represented by the equation

A
2x + 3y = 4

B
x + 2y = 5

C
2x + y = 8

D
3x + 5y = 9

Solution

A given ordered pair lies on a line if it satisfies the equation representing the line.

Consider the equation 2x + y = 8.

On substituting x = 3 and y = 2 in this equation, we observe that

L.H.S = 2x + y = 2 × 3 + 1 × 2 = 6 + 2 = 8 = R.H.S

Hence, the ordered pair (3, 2) satisfies the equation 2x + y = 8.

Thus, point (3, 2) lies on the line represented by the equation 2x + y = 8.

The correct answer is C.
Question 3
1 / -0

Use the following information to answer the next question.

Some linear equations are given as

I. y − 11 = 2

II. x + 3 = 2x − 2

III. 2x = 9

IV. 2y + 5 = 3y − 4

The graph of which of the given equations is parallel to the x-axis?

A
II and IV

B
I and III

C
I and IV

D
II and III

Solution

The graph of an equation of type y = a, where a is constant, is a straight line parallel to the x-axis.

The graph of an equation of type x = b, where b is constant, is a straight line parallel to the y-axis.

I. Consider the equation y − 11 = 2.

y − 11 = 2 ⇒ y = 13, which is of the form y = a. Hence, the graph of this equation is a straight line parallel to the x-axis.

IV. Consider the equation 2y + 5 = 3y − 4.

2y + 5 = 3y − 4

⇒ 2y − 3y = − 4 − 5

⇒ −y = −9

⇒ y = 9, which is of the form y = a. Hence, the graph of this equation is a straight line parallel to the x-axis.

Hence, the graphs of equations I and IV are parallel to the x-axis.

The correct answer is C.
Question 4
1 / -0

Use the following information to answer the next question.

The total cost of 3 identical bottles and 2 identical jugs is Rs 350.

If the cost of a bottle is Rs x and the cost of a jug is Rs y, then which equation is consistent with the given information?

A
3x + 2y = 350

B
3x − 2y = 350

C
2 = 350x + 3y

D
3 = 350y + 2x

Solution

Cost of a bottle = Rs x

Cost of 3 bottles = Rs 3x

Cost of a jug = Rs y

Cost of 2 jugs = Rs 2y

It is given that the total cost of 3 bottles and 2 jugs is Rs 350.

∴ Rs 3x + Rs 2y = Rs 350

Therefore, the given information can be represented in the form of an equation as 3x + 2y = 350.

The correct answer is A.
Question 5
1 / -0

Use the following information to answer the next question.

Ajay and Amit have some number of tennis balls. The number of tennis balls with Amit is 20 less than twice the number of tennis balls with Ajay.

If the number of tennis balls with Ajay and Amit are x and y respectively, then which equation is consistent with the given information?

A
y = 2x − 20

B
x = 2y − 20

C
2x = y − 20

D
2y = x − 20

Solution

Number of tennis balls with Ajay = x

Twice the number of tennis balls with Ajay = 2x

Number of tennis balls with Amit = y

It is given that the number of tennis balls with Amit is 20 less than twice the number of tennis balls with Ajay.

Hence, number of tennis balls with Amit = 2x − 20

Thus, the equation y = 2x − 20 is consistent with the given information.

The correct answer is A.

Question 6

1 / -0

Use the following information to answer the next question.

In laboratories, the temperatures of certain substances are usually measured in Kelvin.

The linear relationship between Kelvin and Celsius is given by the equation

K = C + 273

If the temperature of a certain chemical substance is 238°K, then what is its temperature in Celsius?

−35°C

−34°C

34°C

35°C

Solution

The linear relationship between Kelvin and Celsius is given as

K = C + 273

Temperature of the chemical substance = 238°K

Therefore, the temperature of the substance in Celsius can be obtained by substituting K with 238.

This can be done as

238 = C + 273

⇒ C = 238 − 273 = −35

Thus, the temperature of the substance in Celsius is −35°C.

The correct answer is A.

Question 7
1 / -0

The equation 3y = 2x + 3 has

A
two solutions

B
three solutions

C
a unique solution

D
infinitely many solutions

Solution

The equation 3y = 2x + 3 is a linear equation in two variables i.e., x and y.

We know that a linear equation in two variables has infinitely many solutions.

Thus, the equation 3y = 2x + 3 has infinitely many solutions.

The correct answer is D.
Question 8
1 / -0

Which of the following ordered pairs is not a solution of the equation 2x + y = 8?

A
(2, 4)

B
(3, 3)

C
(4, 0)

D
(3, 2)

Solution

The given equation is 2x + y = 8.

Consider the order pair (3, 3):

On substituting x = 3 and y = 3 in the given equation, we observe that

L.H.S. = 2x + y = 2 × 3 + 3 = 6 + 3 = 9 ≠ R.H.S.

Hence, the ordered pair (3, 3) does not satisfy the given equation.

Thus, the ordered pair (3, 3) is not a solution of the given equation.

The correct answer is B.
Question 9
1 / -0

Which of the following ordered pairs is a solution of the equation 6x + 7y = 26?

A
(3, 3)

B
(1, 3)

C
(2, 2)

D
(0, 4)

Solution

The given equation is 6x + 7y = 26.

Consider the order pair (2, 2).

On substituting x = 2 and y = 2 in the given equation, we observe that

L.H.S. = 6x + 7y = 6 × 2 + 7 × 2 = 12 + 14 = 26 = R.H.S.

Hence, the ordered pair (2, 2) satisfies the given equation.

Thus, the ordered pair (2, 2) is a solution of the given equation.

The correct answer is C.
Question 10
1 / -0

After 3 years, David’s age will be twice Nelson’s age. If David and Nelson’s present ages are x years and y years respectively, then which equation is consistent with the given information?

A
x − 3y = 2

B
3x −y = 2

C
x − 2y = 3

D
2x − y = 3

Solution

David’s present age = x years

Nelson’s present age = y years

Accordingly, after 3 years, David’s age will be (x + 3) years and Nelson’s age will be (y + 3) years.

It is given that after 3 years David’s age will be twice Nelson’s age.

∴x + 3 = 2(y + 3)

⇒ x + 3 = 2y + 6

⇒ x − 2y = 6 − 3

⇒ x − 2y = 3

Thus, the required equation is x − 2y = 3.

Hence, the correct answer is option C.
Question 11
1 / -0

Use the following information to answer the next question.

The sum of the cost of 12 mangoes and 5 apples is Rs 100. The cost of each mango and each apple is equal.

If the cost of each mango is Rs x and cost of each apple is Rs y, then which equation represents given information?

A
5x + 12y = 100

B
5x − 12y = 100

C
12x − 5y = 100

D
12x + 5y = 100

Solution

Cost of each mango = Rs x

∴Cost of 12 mangoes = Rs 12x

Cost of each apple = Rs y

∴Cost of 5 apples = Rs 5y

It is given that the sum of the cost of 12 mangoes and 5 apples is Rs 100.

Therefore, the given information can be represented by the relationship

12x + 5y = 100

The correct answer is D.

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Linear Equations in Two Variables Test - 15

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Linear Equations in Two Variables Test - 15

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Question 1

x = 200 + 40y

x = 40 + 200y

y = 200 + 40x

y = 40 + 200x

Solution

Question 2

2x + 3y = 4

x + 2y = 5

2x + y = 8

3x + 5y = 9

Solution

Question 3

II and IV

I and III

I and IV

II and III

Solution

Question 4

3x + 2y = 350

3x − 2y = 350

2 = 350x + 3y

3 = 350y + 2x

Solution

Question 5

y = 2x − 20

x = 2y − 20

2x = y − 20

2y = x − 20

Solution

Question 6

−35°C

−34°C

34°C

35°C

Solution

Question 7

two solutions

three solutions

a unique solution

infinitely many solutions

Solution

Question 8

(2, 4)

(3, 3)

(4, 0)

(3, 2)

Solution

Question 9

(3, 3)

(1, 3)

(2, 2)

(0, 4)

Solution

Question 10

x − 3y = 2

3x −y = 2

x − 2y = 3

2x − y = 3

Solution

Question 11

5x + 12y = 100

5x − 12y = 100

12x − 5y = 100

12x + 5y = 100

Solution

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