Worksheet on Linear Equations in Two Variables Class 10 have been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 10. Students are always suggested to solve printable worksheets for Mathematics Linear Equations Grade 10 as they can be really helpful to clear their concepts and improve problem solving skills. We at worksheetsbag.com have provided here free PDF worksheets for students in standard 10 so that you can easily take print of these test sheets and use them daily for practice. All worksheets are easy to download and have been designed by teachers of Class 10 for benefit of students and is available for free download.

## Mathematics Linear Equations Worksheets for Class 10

We have provided **chapter-wise worksheets for class 10 Mathematics Linear Equations** which the students can download in Pdf format for free. This is the best collection of Mathematics Linear Equations standard 10th worksheets with important questions and answers for each grade 10th Mathematics Linear Equations chapter so that the students are able to properly practice and gain more marks in Class 10 Mathematics Linear Equations class tests and exams.

### Chapter-wise Class 10 Mathematics Linear Equations Worksheets Pdf Download

**Question. In the equations 3x + 2y = 13xy and 4x -5y = 2xy , the value of xand y satisfy that the equations are: C**

(A) (2,3)

(B) (3,2)

(C) (1/2,1/3)

(D) (1/3,1/2)

**Answer**

C

**Question. A father is 7 times as old as his son. Two year ago, the father was 13 times as old as his son. Father’s present age is: **

(A) 24 years

(B) 28 years

(C) 30 years

(D) 32 years

**Answer**

B

**Question. If x + y + 7and3x -2y=11. Then the value of x will be: **

(A) 5

(B) 6

(C) 7

(D) 8

**Answer**

A

**Question. If 3y -2x = 4and4y – px = 2perpendicular to each other the value of ‘p’ will be: **

(A) 3/2

(B) 8/3

(C) 6

(D) -6

**Answer**

D

**Question. A boat whose speed is 18km/hr in still water takes 1 hr more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream. **

(A) 8 km/hr

(B) 6 km/hr

(C) 10 km/hr

(D) 5.5 km/hr

**Answer**

B

**Question. It is given that there is no solution to the system x + 2y = 3,ax +by = 4 . Which one of the following is true? **

(A) a has a unique value

(B) b has a unique value

(C) a can have more than one value

(D) a has exactly two different values

**Answer**

C

**Question. In a two digit number, the number of ten’s place is double of the number of unit’s place. If we exchange the numbers mutually then the number decrease b 18, then the number is:- **

(A) 24

(B) 36

(C) 39

(D) 42

**Answer**

D

**Question. The system of equation- x + 2y = 6,3x +6y=18 **

(A) Is inconsistent

(B) Has an infinite number of solution

(C) Has a unique solution

(D) None of these

**Answer**

B

**Question. A man can row three quarters of a km against the stream in 11(1/4) minutes and return in 7(1/2) minutes. The speed of man in still water is: **

(A) 2 km/h

(B) 3 km/h

(C) 4 km/h

(D) 5 km/h

**Answer**

D

**Solved Problems on Class 10 Linear Equations**

**Question. What are the coordinates of points where two lines representing the given equations meet y-axis?**

**Answer**

(0, –2), (0, 4)

**Question. The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.**

**Answer**

4/7

**Question**. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

**Answer**

Father’s age = 42 years, Son’s age = 10 years

**Question**. Determine graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8.

**Answer**

(0, 0), (4, 4) (6, 2)

**Question. If a1/a2≠b1/b2≠c1/c2 , then what does the system of linear equations, represent graphically?**

**Answer**

Two coincident lines

**Question**. The cost of 4 pens and 4 pencil boxes is ` 100. Three times the cost of a pen is ` 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

**Answer**

10, ` 15

**Question**. **The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.**

**Answer**

36

**Question. Define consistent system of linear equations.**

## An**swer**

A pair of linear equations which has either unique or infinitely many solutions.

**Question. What is the solution of given pair of equations? Read from graph.**

**Answer**

Unique solution: (3, 1)

**Question**. The sum of a two digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3, find the number.

**Answer**

69 or 96

**Question** A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

**Answer**

2.5 km/h

**Question**. **Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.**

**Answer**

Speed from point A = 40 km/ h, from point B = 30 km/h

**Question**. **Yash scored 35 marks in a test, getting 2 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?**

**Answer**

25

**Question**. **Draw the graphs of the equations y = -1, y = 3 and 4x – y = 5. Also, find the area of the quadrilateral formed by the lines and the y-axis.**

**Answer**

6 square units

**Question. What does a linear equation in two variables represent geometrically?**

## An**swer**

A straight line.

**Question. What is the area of triangle formed by given lines and x-axis?**

**Answer**

1 sq. unit

**Question**. A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

**Answer**

100 km/h, 80 km/h

**Question**. Solve graphically the system of linear equations:**(ii) 4x-3y+4=0****4x-3y+20= 0****Find the area bounded by these lines and x-axis.**

**Answer**

x = 2, y = 4, 12 sq. units

**Question**. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.

**Answer**

10 km/h, 40 km/h

**Question. When is a system of linear equations called inconsistent?**

**Answer**

When it has no solution.

**Question**.**A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 15 days, he has to pay 1200 as hostel charges whereas a student B, who takes food for 24 days, pays 1560 as hostel charges. Find the fixed charge and the cost of food per day.**

**Answer**

₹ 600, ₹ 40

**Question**. Solve the following system of linear equations graphically and shade the region between the two lines and x-axis.**(i) 3x+2y-4=0 (ii) 3x+2y-11=0****2x-3y+10= 0 2x-3y-7= 0**

**Answer**

(i) x = 2, y = -1 (ii) x =1, y = 4

**Question. Do the equations x +2y -7 = 0 and 2x + 4 y +5= 0 represent a pair of parallel lines?**

**Answer**

Yes

**Question. 2 women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone, and that taken by 1 man alone to finish the embroidery.**

**Answer**

One man in 36 days, One woman in 18 days

**Question. Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum respectively. She received 1860 as annual interest. However, had she interchanged the amount of investment in the two schemes, she would have received 20 more as annual interest. How much money did she invest in each scheme?**

**Answer**

Scheme A ₹ 12000, Scheme B ₹ 10,000

**Question. What is the area of triangle formed by given lines and y-axis?**

**Answer**

9 sq. units

**Question. The car hire charges in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is 89 and for a journey of 20 km, the charge paid is 145. What will a person have to pay for travelling a distance of 30 km?**

**Answer**

₹ 215

**Question. Is it true to say that the pair of equations x +2y -3 = 0 and 3x +6 y -9 = 0 are dependent?**

## A**nswer**

Yes

**Question. A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.**

**Answer**

36

**Question. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars?**

**Answer**

60 km/h, 40 km/h

**Question. If lines corresponding to two given linear equations are coincident, what can you say about the solution of the system of given equations?**

**Answer**

It has infinitely many solutions.

**Question. What are the coordinates of points where two lines representing the given equations meet x-axis?**

**Answer**

(2, 0), (4, 0)

## Mathematics Linear Equations Worksheets for Class 10 as per CBSE NCERT pattern

Parents and students are welcome to download as many worksheets as they want as we have provided all free. As you can see we have covered all topics which are there in your Class 10 Mathematics Linear Equations book designed as per CBSE, NCERT and KVS syllabus and examination pattern. These test papers have been used in various schools and have helped students to practice and improve their grades in school and have also helped them to appear in other school level exams. You can take printout of these chapter wise test sheets having questions relating to each topic and practice them daily so that you can thoroughly understand each concept and get better marks. As Mathematics Linear Equations for Class 10 is a very scoring subject, if you download and do these questions and answers on daily basis, this will help you to become master in this subject.

**Benefits of Free Worksheet on Linear Equations in Two Variables Class 10**

- You can improve understanding of your concepts if you solve NCERT Class 10 Mathematics Linear Equations Worksheet,
- These CBSE Class 10 Mathematics Linear Equations worksheets can help you to understand the pattern of questions expected in Mathematics Linear Equations exams.
- All worksheets for Mathematics Linear Equations Class 10 for NCERT have been organized in a manner to allow easy download in PDF format
- Parents will be easily able to understand the worksheets and give them to kids to solve
- Will help you to quickly revise all chapters of Class 10 Mathematics Linear Equations textbook
- CBSE Class 10 Mathematics Linear Equations Workbook will surely help to improve knowledge of this subject

These Printable practice worksheets are available for free download for Class 10 Mathematics Linear Equations. As the teachers have done extensive research for all topics and have then made these worksheets for you so that you can use them for your benefit and have also provided to you for each chapter in your ebook. The Chapter wise question bank and revision worksheets can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 10 Mathematics Linear Equations Worksheets PDF.

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**I want free printable worksheets with questions and answers for Mathematics Linear Equations for Standard 10, where can I get them?**

You can get free PDF downloadable worksheets for Grade 10 Mathematics Linear Equations from our website which has been developed by teachers after doing extensive research in each topic.

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On our website we have provided worksheets for all subjects in Grade 10, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

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