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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
3: Expansions
4: Factorisation
▶ 5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
19: Trigonometry
20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 5 - Simultaneous Linear Equations - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 5 - Simultaneous Linear Equations")
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Solutions for Chapter 5: Simultaneous Linear Equations
Below listed, you can find solutions for Chapter 5 of CISCE B Nirmala Shastry for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 5 Simultaneous Linear Equations EXERCISE 5A [Page 53]
Solve the following pair of simultaneous equations.
3x + y = 2, 2x + 3y = 20
Solve the following pair of simultaneous equations.
9x − 5y = 52, 4x − 3y = 27
Solve the following pair of simultaneous equations.
3x − 2y = 9, `x/2 - y/6 = 5/6`
Solve the following pair of simultaneous equations.
`(2x)/3 + (3y)/4 = 7`, 5x = 3y + 18
Solve the following pair of simultaneous equations.
`x/2 + y/3 = 9 and x/5 - y/4 = -1`
Solve the following pair of simultaneous equations.
3x + 2.6y = 16 and x + 5.2y = 27
Solve the following pair of simultaneous equations.
73x + 27y = 19, 27x + 73y = −119
Solve the following pair of simultaneous equations.
31x + 37y = 25, 37x + 31y = 43
Solve the following pair of simultaneous equations.
43x + 31y = 98, 31x + 43y = 50
Solve the following pair of simultaneous equations.
65x + 49y = 293, 49x + 65y = 277
Solve the following pair of simultaneous equations.
`4x + 3/y = 18, 3x + 2/y = 13`
Solve the following pair of simultaneous equations.
`5/x - 3y = 7, 3/x - 2y = 4`
Solve the following pair of simultaneous equations.
`7/x + 6/y = 71, 5/x - 8/y = -23`
Solve the following pair of simultaneous equations.
`8/x + 5/y = -3, 6/x + 25/y = 2`
Solve the following pair of simultaneous equations.
`15/x + 4/y = 7, 9/x - 8/y = -1`
Solve the following pair of simultaneous equations.
`2/x + 1/y = 10, 3/x - 2/y = 1`
Solve the following pair of equations by cross multiplication method.
4x − 5y + 7 = 0, 3x − 4y + 6 = 0
Solve the following pair of equations by cross multiplication method.
5x − 2y + 9 = 0, 4x + 3y = 2
Solve the following pair of equations by cross multiplication method.
7x − y = 23, 8x + 3y = 18
Solve the following pair of equations by cross multiplication method.
9x + 5y = 7, 6x − y = 22
Solve the following pair of equations by cross multiplication method.
11x + 5y = 7, 6x − 3y = 21
Solve the following pair of equations by cross multiplication method.
2x − 5y = 14, x + 2y + 2 = 0
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 5 Simultaneous Linear Equations EXERCISE 5B [Pages 59 - 60]
Problems on Numbers:
The difference between two numbers is 4 and six times the smaller is equal to four times the greater. Find the numbers.
The sum of two numbers is 48, and five times the smaller number is equal to three times the greater number. Find the numbers.
Find two numbers such that the sum of thrice the first number and twice the second number is 102. Also, five times the first number exceeds thrice the second number by 18. Find the numbers.
Two numbers are in the ratio 4 : 7. If 4 is subtracted from each of the numbers, then the ratio becomes 7 : 13. Find the numbers.
Two numbers are in the ratio 3 : 5. If 5 is added to each of the numbers, then the ratio becomes 2 : 3. Find the numbers.
The sum of two numbers is 20, and the difference of their squares is 80. Find the numbers.
Problems on Age:
The sum of the present ages of Rani and her father is 43 years. Six years hence, father will be 4 times as old as his daughter. Find their present ages.
Five years ago, a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.
The sum of the ages of Arunima and Kareena is 64 years. Arunima is 6 years older than Kareena. Find their present ages.
Five years ago, A’s age was 5 years less than twice B’s age. Three years from now, one-third of B’s age will be 12 years less than A’s age. Find their present ages.
Problems on Two-digit Numbers:
A two-digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.
When a two-digit number is divided by the sum of its digits, the quotient is 4. If the digits are interchanged, the reversed number is 6 less than twice the original number. Find the number.
The sum of the digits of a two-digit number is 7. When the digits are interchanged, the reversed number is 5 times the ten’s digit of the original number. Find the original number.
The sum of a two-digit number and the number obtained by interchanging the digits is 154. If the ten’s digit is 2 more than unit’s digit, find the original number.
The sum of the digits of a two-digit number is 8. If the digits are interchanged, new number is 10 more than double the original number. Find the original number.
A two-digit number becomes `5/6` of the reversed number obtained when the digits are interchanged. The difference between the digits is 1. Find the number.
Problems on Geometry:
ABC is an equilateral triangle. If AB = 2x − 1, BC = y + 7, AC = 2y + 3, find x and y.
If the length of a rectangle is increased by 12 cm and the width is decreased by 8 cm, the area is unchanged. If the original length is increased by 5 cm and the original width is decreased by 4 cm, also the area remains the same. Find the original dimensions.
The length of a rectangle is greater than 4 times its breadth by 5cm. If its length is reduced by 2cm and breadth is increased by 2cm, then the area of the rectangle increases by 36cm2. Find the length and breadth of the original rectangle.
The area of a rectangle decreases by 10cm2 if the length is decreased by 5cm and the breadth is increased by 3cm. If the length is increased by 5cm and the breadth is increased by 2cm, then the area increases by 80cm2. Find the perimeter of the rectangle.
Problems on Fractions:
Find the fraction which becomes `1/2` when the denominator is increased by 1 and is equal to `2/3` when both the numerator and denominator are increased by 4.
When the numerator of a fraction is increased by 2 and the denominator by 1, the fraction becomes equal to `5/8`, and if the numerator and denominator 8 are each diminished by 1, the fraction becomes `1/2`. Find the fraction.
A fraction’s value is `4/5`. When its numerator is increased by 9, the new fraction equals the reciprocal of the value of the original fraction. Find the original fraction.
Problems on Speed:
A boat takes 6 hours to travel 36 km upstream, and it takes 3 hours to travel 30 km downstream. Find the speed of the boat in still water and the speed of the stream.
A plane can fly 1120km in 1 hour 20 minutes with the wind. Flying against the same wind, the plane travels the same distance in 1 hour 24 minutes. Find the speed of the plane and the speed of the wind.
If Laisha walks for 1 hour and cycles for 2 hours, she can travel 33 km. But if she walks for 2 hours and cycles for 1 hour, she can cover 24 km. What are her walking and cycling speeds?
An aeroplane takes 3 hours to fly 1200 km against the wind. The return trip takes 2 hours. Find the speed of the plane in still air and the wind speed.
Maheep travels 600 km partly by train and partly by car. He takes 8 hours to cover the whole distance if he travels 120 km by train and rest by car. But he takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speed of train and car.
Two towns, A and B, are 120 km apart on the highway. One car starts from A and the other from B at the same time, at different speeds. If the cars travel in the same direction, the cars meet in 4 hours. But when they travel towards each other, they meet in 1 hour. Find their speeds.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 5 Simultaneous Linear Equations MULTIPLE CHOICE QUESTIONS [Pages 60 - 61]
The solution for equations x + y = 3 and x − y = 7 is ______.
(2, 1)
(5, −2)
(5, 2)
(4, −1)
Which of the following satisfy the equations x − 2y = 7 and 3x + 2y = 5?
(7, 0)
(3, −2)
(3, 2)
(1, 1)
`8/x + 5y = 11 and 4/x + 3y = 7` have solution ______.
`(1/2, -1)`
(2, −3)
`(1/4, -3)`
(−2, 3)
The sum of 2 numbers is 15, and their difference is 3. Therefore, the numbers are ______.
(17, −2)
(8, 7)
(9, 6)
(6, 9)
The sum of 2 numbers is 36. One number is twice the other. Therefore, the numbers are ______.
(19, 17)
(6, 30)
(26, 10)
(12, 24)
The sum of 2 numbers is 75. If one exceeds the other by 13, the numbers are ______.
(45, 30)
(44, 31)
(40, 35)
(41, 34)
One number is 6 times the other. If their difference is 90, the numbers are ______.
(12, 72)
(13, 78)
(18, 108)
(10, 100)
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.
27
72
45
36
Ameena has 40 coins of ₹2 and ₹5. The amount of her money is ₹116. Find the number of ₹2 and ₹5 coins.
20, 20
30, 10
25, 15
28, 12
Mother’s age is 7 times her son’s age. After 2 years, she will be 5 times his age.
∴ Their present ages are ______.
(3, 21)
(5, 35)
(4, 28)
(6, 42)
The sum of the digits of a 2-digit number is 13. When 27 is subtracted from it, the digits get reversed. Find the number.
94
49
58
85
The sum of 2 numbers is 120, and their ratio is 2:3. Find the numbers.
(40, 80)
(50, 70)
(36, 84)
(48, 72)
The sum of 2 numbers is 18, and their difference is 8. Therefore, the product of numbers is ______.
80
77
65
72
The sum of 2 numbers is 9. The difference of their squares is also 9. The two numbers are ______.
6, 3
7, 2
5, 4
8, 1
In the figures height of the bird is?
 |
 |
30
20
15
10
If glass full of water weighs 600 g and half a glass of water weight 350 g, what is the weight of the empty glass?
 |
 |
100 g
150 g
200 g
300 g
If 2 tables and 4 chairs cost ₹2,800, then the cost of 5 tables and 10 chairs will be ______.
₹8,400
₹7,000
₹7,500
₹11,200
In each of the following questions, a statement of assertion (A) is given and a statement of Reason (R) given below it. Choose the correct option for each question.
Assertion (A): (2, −1) is the solution to the two equations 3x + 4y = 2 and 7x − 2y = 16.
Reason (R): A system of linear or equations is said to be consistent and independent if there exists only one solution.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): If x = 2k and y = k − 1 is a solution of 3x − 5y = 7, then k = 2.
Reason (R): A linear equation in 2 variables has infinitely many solutions.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): The graph of equation 2x − y = 1 passes through the point (2, 3).
Reason (R): Every point lying on the graph of 2x − y = 1 is not a solution of 2x − y = 1.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): x − 3y = 7 and 5x − 15y = 10 have no solution.
Reason (R): Parallel lines have no solution.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): `8/x + 5y = 11, and 4/x + 3y = 5` have solution `(1/2, -1).`
Reason (R): `(1/2,-1)` satisfies both the equations.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 5 Simultaneous Linear Equations MISCELLANEOUS EXERCISE [Pages 61 - 62]
Solve each pair of equations given below:
`x/3 + y/2 = 4, x/2 + y/4 = 4`
97x − 78y = 310, 78x − 97y = 215
`14/x + 3/y = 5, 21/x - 8/y = -5`
Amrita came first in x races and second in y races. A score of 5 points is given for coming first and 3 points for the second place in a race. She scored 34 points, but if the number of games in which she came first and second were interchanged, she would have scored 4 points less. Find x and y.
For a school concert, 210 tickets are sold. Of the tickets, some were for adults and others for students. The total money collected is ₹4300. If adult ticket costs ₹25 each and student ticket costs ₹15 each, find the number of tickets sold of each kind.
An instructor scored a student’s test of 50 questions by giving 2 marks for a right answer and −1 for a wrong answer. If the score is 76, find out the number of right answers.
The cost of 5 pens and 8 notebooks is ₹160, whereas the cost of 9 pens and 6 notebooks is ₹162. Find the cost of each.
For a club anniversary dinner, some members and some of their guests attended the dinner. The guests were `1/3` of the number of members. Each guest paid ₹400, and each member paid ₹300. The total sum collected for the event was ₹1,04,000. Find the number of members who attended the event.
Pramod is 25 kg heavier than his wife, Pranita. After a dieting course, Pramod loses 20 kg and Pranita loses 15 kg, and their total weight is 140 kg. Find their original weight.
In a farmyard, there were some goats and some chickens. When their number was counted, it was found that there were 60 heads and 148 legs. How many goats and how many chickens were in the farmyard?
The sum of the numerator and denominator of a fraction is 2 more than twice the numerator. If the numerator and the denominator are reduced by 3, they are in the ratio 3 : 4. Find the fraction.
2 men and 7 boys complete a certain piece of work in 8 days. 4 men and 4 boys can do the same in only 6 days. Find the number of days required to complete the work by 1 man.
A boat takes 2 hours to go 24 km downstream and takes 3 hours to return, moving 24 km upstream. Find the speed of the boat in still water.
In ABC, AB = AC and A = 60°. AB = 3x + 5, BC = 3y + 2 and AC = 7x − 11. Find the values of x and y.
A certain number of two-rupee coins and a certain number of five-rupee coins in a piggy bank of a child amount to ₹47. If the number of each kind are interchanged, they would amount to ₹3 less than before. Find the number of coins of each kind.
Solutions for 5: Simultaneous Linear Equations
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 5 - Simultaneous Linear Equations
Shaalaa.com has the CISCE Mathematics मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. B Nirmala Shastry solutions for Mathematics मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई CISCE 5 (Simultaneous Linear Equations) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. B Nirmala Shastry textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 5 Simultaneous Linear Equations are Methods of Solving Simultaneous Linear Equations by Elimination Method, Method of Elimination by Equating Coefficients, Equations Reducible to Linear Equations, Methods of Solving Simultaneous Linear Equations by Elimination Method, Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method, Simultaneous linear equations, Pair of Linear Equations in Two Variables, Word Problems on Linear Equations, Graphical Method with Different Cases of Solution.
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