# NCERT solutions for Mathematics Exemplar Class 10 chapter 3 - Pair of Liner Equation in Two Variable [Latest edition]

#### Chapters ## Chapter 3: Pair of Liner Equation in Two Variable

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4
Exercise 3.1 [Pages 18 - 19]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 3 Pair of Liner Equation in Two Variable Exercise 3.1 [Pages 18 - 19]

#### Choose the correct alternative:

Exercise 3.1 | Q 1 | Page 18

Graphically, the pair of equations 6x – 3y + 10 = 0, 2x – y + 9 = 0 represents two lines which are ______.

• Intersecting at exactly one point

• Intersecting at exactly two points

• Coincident

• Parallel

Exercise 3.1 | Q 2 | Page 18

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have ______.

• A unique solution

• Exactly two solutions

• Infinitely many solutions

• No solution

Exercise 3.1 | Q 3 | Page 18

If a pair of linear equations is consistent, then the lines will be ______.

• Parallel

• Parallel

• Always coincident

• Always coincident

• Intersecting or coincident

• Intersecting or coincident

• Always intersecting

• Always intersecting

Exercise 3.1 | Q 4 | Page 18

The pair of equations y = 0 and y = –7 has ______.

• One solution

• Two solutions

• Infinitely many solutions

• No solution

Exercise 3.1 | Q 5 | Page 18

The pair of equations x = a and y = b graphically represents lines which are ______.

• Parallel

• Intersecting at (b, a)

• Coincident

• Intersecting at (a, b)

Exercise 3.1 | Q 6 | Page 18

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

• 1/2

• -1/2

• 2

• –2

Exercise 3.1 | Q 7 | Page 19

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is ______.

• (-5)/4

• 2/5

• 15/4

• 3/2

Exercise 3.1 | Q 8 | Page 19

The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is ______.

• 3

• – 3

• –12

• No value

Exercise 3.1 | Q 9 | Page 19

One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be ______.

• 10x + 14y + 4 = 0

• –10x – 14y + 4 = 0

• –10x + 14y + 4 = 0

• 10x – 14y = –4

Exercise 3.1 | Q 10 | Page 19

A pair of linear equations which has a unique solution x = 2, y = –3 is ______.

• x + y = –1, 2x – 3y = –5

• 2x + 5y = –11, 4x + 10y = –22

• 2x – y = 1, 3x + 2y = 0

• x – 4y –14 = 0, 5x – y – 13 = 0

Exercise 3.1 | Q 11 | Page 19

If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively ______.

• 3 and 5

• 5 and 3

• 3 and 1

• –1 and –3

Exercise 3.1 | Q 12 | Page 19

Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively ______.

• 35 and 15

• 35 and 20

• 15 and 35

• 25 and 25

Exercise 3.1 | Q 13 | Page 19

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively ______.

• 4 and 24

• 5 and 30

• 6 and 36

• 3 and 24

Exercise 3.2 [Pages 21 - 22]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 3 Pair of Liner Equation in Two Variable Exercise 3.2 [Pages 21 - 22]

Exercise 3.2 | Q 1.(i) | Page 21

Do the following pair of linear equations have no solution? Justify your answer.

2x + 4y = 3, 12y + 6x = 6

Exercise 3.2 | Q 1.(ii) | Page 21

Do the following pair of linear equations have no solution? Justify your answer.

x = 2y, y = 2x

Exercise 3.2 | Q 1.(iii) | Page 21

Do the following pair of linear equations have no solution? Justify your answer.

3x + y - 3 = 0, 2x + 2/3y = 2

Exercise 3.2 | Q 2.(i) | Page 21

Do the following equations represent a pair of coincident lines? Justify your answer.

3x + 1/7 y = 3, 7x + 3y = 7

Exercise 3.2 | Q 2.(ii) | Page 21

Do the following equations represent a pair of coincident lines? Justify your answer.

–2x – 3y = 1, 6y + 4x = – 2

Exercise 3.2 | Q 2.(iii) | Page 21

Do the following equations represent a pair of coincident lines? Justify your answer.

x/2 + y + 2/5 = 0, 4x + 8y + 5/16 = 0

Exercise 3.2 | Q 3.(i) | Page 21

–3x – 4y = 12, 4y + 3x = 12

Exercise 3.2 | Q 3.(ii) | Page 21

3/5x - y = 1/2

Exercise 3.2 | Q 3.(iii) | Page 21

2ax + by = a, 4ax + 2by – 2a = 0; a, b ≠ 0

Exercise 3.2 | Q 3.(iv) | Page 21

x + 3y = 11, 2(2x + 6y) = 22

Exercise 3.2 | Q 4 | Page 21

For the pair of equations λx + 3y = –7, 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true? Give reasons.

Exercise 3.2 | Q 5 | Page 22

For all real values of c, the pair of equations x – 2y = 8, 5x – 10y = c have a unique solution. Justify whether it is true or false.

• True

• False

Exercise 3.2 | Q 6 | Page 22

The line represented by x = 7 is parallel to the x–axis. Justify whether the statement is true or not.

• True

• Not true

Exercise 3.3 [Pages 25 - 28]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 3 Pair of Liner Equation in Two Variable Exercise 3.3 [Pages 25 - 28]

Exercise 3.3 | Q 1.(ii) | Page 25

For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have infinitely many solutions?

Exercise 3.3 | Q 1.(iii) | Page 25

For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have a unique solution?

Exercise 3.3 | Q 2 | Page 25

For which value(s) of k will the pair of equations kx + 3y = k – 3, 12x + ky = k have no solution?

Exercise 3.3 | Q 3 | Page 25

For which values of a and b, will the following pair of linear equations have infinitely many solutions?

x + 2y = 1, (a – b)x + (a + b)y = a + b – 2

Exercise 3.3 | Q 4.(i) | Page 25

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.

Exercise 3.3 | Q 4.(ii) | Page 25

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

– x + py = 1 and px – y = 1, if the pair of equations has no solution.

Exercise 3.3 | Q 4.(iii) | Page 25

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

– 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point.

Exercise 3.3 | Q 4.(iv) | Page 25

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Exercise 3.3 | Q 4.(v) | Page 25

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations have infinitely many solutions.

Exercise 3.3 | Q 5 | Page 26

Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.

Exercise 3.3 | Q 6 | Page 26

Write a pair of linear equations which has the unique solution x = – 1, y =3. How many such pairs can you write?

Exercise 3.3 | Q 7 | Page 26

If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and y/x – 2.

Exercise 3.3 | Q 8 | Page 26

Find the values of x and y in the following rectangle [see figure]. Exercise 3.3 | Q 9.(i) | Page 26

Solve the following pair of equations:

x + y = 3.3, 0.6/(3x - 2y) = -1, 3x - 2y ≠ 0

Exercise 3.3 | Q 9.(ii) | Page 26

Solve the following pair of equations:

x/3 + y/4 = 4, (5x)/6 - y/4 = 4

Exercise 3.3 | Q 9.(iii) | Page 26

Solve the following pair of equations:

4x + 6/y = 15, 6x - 8/y = 14, y ≠ 0

Exercise 3.3 | Q 9.(iv) | Page 26

Solve the following pair of equations:

1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8,   x, y ≠ 0

Exercise 3.3 | Q 9.(v) | Page 26

Solve the following pair of equations:

43x + 67y = – 24, 67x + 43y = 24

Exercise 3.3 | Q 9.(vi) | Page 26

Solve the following pair of equations:

x/a + y/b = a + b, x/a^2 + y/b^2 = 2,  a, b ≠ 0

Exercise 3.3 | Q 9.(vii) | Page 26

Solve the following pair of equations:

(2xy)/(x + y) = 3/2, (xy)/(2x - y) = (-3)/10,  x + y ≠ 0, 2x - y ≠ 0

Exercise 3.3 | Q 10 | Page 27

Find the solution of the pair of equations x/10 + y/5 - 1 = 0 and x/8 + y/6 = 15. Hence, find λ, if y = λx + 5.

Exercise 3.3 | Q 11.(i) | Page 27

By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

3x + y + 4 = 0, 6x – 2y + 4 = 0

Exercise 3.3 | Q 11.(ii) | Page 27

By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

x – 2y = 6, 3x – 6y = 0

Exercise 3.3 | Q 11.(iii) | Page 27

By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

x + y = 3, 3x + 3y = 9

Exercise 3.3 | Q 12 | Page 27

Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Exercise 3.3 | Q 13 | Page 27

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1. How many such lines can we find?

Exercise 3.3 | Q 14 | Page 27

If (x + 1) is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a – 3b = 4.

Exercise 3.3 | Q 15 | Page 27

The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.

Exercise 3.3 | Q 16 | Page 28

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Exercise 3.3 | Q 17 | Page 28

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Exercise 3.3 | Q 18 | Page 28

Two numbers are in the ratio 5 : 6. If 8 is subtracted from the numbers, the ratio becomes 4 : 5. Find the numbers.

Exercise 3.3 | Q 19 | Page 28

There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.

Exercise 3.3 | Q 20 | Page 28

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

Exercise 3.3 | Q 21 | Page 28

In a competitive examination, one mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Exercise 3.3 | Q 22 | Page 28

The angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, and ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles.

Exercise 3.4 [Pages 33 - 34]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 3 Pair of Liner Equation in Two Variable Exercise 3.4 [Pages 33 - 34]

Exercise 3.4 | Q 1 | Page 33

Graphically, solve the following pair of equations:

2x + y = 6
2x – y + 2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Exercise 3.4 | Q 2 | Page 33

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

Exercise 3.4 | Q 3 | Page 33

Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x–axis.

Exercise 3.4 | Q 4 | Page 33

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 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.

Exercise 3.4 | Q 5 | Page 33

Determine, algebraically, the vertices of the triangle formed by the lines

3x – y = 2
2x – 3y = 2
x + 2y = 8

Exercise 3.4 | Q 6 | Page 33

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.

Exercise 3.4 | Q 7 | Page 34

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.

Exercise 3.4 | Q 8 | Page 34

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Exercise 3.4 | Q 9 | Page 34

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Exercise 3.4 | Q 10 | Page 34

A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.

Exercise 3.4 | Q 11 | Page 34

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.

Exercise 3.4 | Q 12 | Page 34

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 Rs 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 20 more as annual interest. How much money did she invest in each scheme?

Exercise 3.4 | Q 13 | Page 34

Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.

## Chapter 3: Pair of Liner Equation in Two Variable

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4 ## NCERT solutions for Mathematics Exemplar Class 10 chapter 3 - Pair of Liner Equation in Two Variable

NCERT solutions for Mathematics Exemplar Class 10 chapter 3 (Pair of Liner Equation in Two Variable) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 10 chapter 3 Pair of Liner Equation in Two Variable are Relation Between Co-efficient, Inconsistency of Pair of Linear Equations, Algebraic Conditions for Number of Solutions, Simple Situational Problems, Pair of Linear Equations in Two Variables, Graphical Method of Solution of a Pair of Linear Equations, Substitution Method, Elimination Method, Cross - Multiplication Method, Equations Reducible to a Pair of Linear Equations in Two Variables, Consistency of Pair of Linear Equations, Linear Equation in Two Variables.

Using NCERT Class 10 solutions Pair of Liner Equation in Two Variable exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 3 Pair of Liner Equation in Two Variable Class 10 extra questions for Mathematics Exemplar Class 10 and can use Shaalaa.com to keep it handy for your exam preparation