Chapter 8 : Simultaneous Linear Equations - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 8 - Simultaneous Linear Equations Excercise Ex. 8.1

Question 1

Solve the following simultaneous equations by the substitution method:

2x + y = 8

3y = 3 + 4x

Solution 1

Question 2

Solve the following simultaneous equations by the substitution method:

x + 3y= 5

7x - 8y = 6

Solution 2

Question 3

Solve the following simultaneous equations by the substitution method: 5x + 4y - 23 = 0

x + 9 = 6y

Solution 3

Question 4

Solve the following simultaneous equations by the substitution method:

2x + 3y = 31

5x - 4 = 3y

Solution 4

Question 5

Solve the following simultaneous equations by the substitution method:

7x - 3y = 31

9x - 5y = 41

Solution 5

Question 6

Solve the following simultaneous equations by the substitution method:

13 + 2y = 9x

3y = 7x

Solution 6

Question 7

Solve the following simultaneous equations by the substitution method:

0.5x + 0.7y = 0.74

0.3x + 0.5y = 0.5

Solution 7

Question 8

Solve the following simultaneous equations by the substitution method:

0.4x + 0.3y = 1.7

0.7x - 0.2y = 0.8

Solution 8

 

 

Question 9

Solve the following simultaneous equations by the substitution method:

3 - (x + 5) = y + 2

2(x + y) = 10 + 2y

Solution 9

Question 10

Solve the following simultaneous equations by the substitution method:

7(y + 3) - 2(x + 2) = 14

4(y - 2) + 3(x - 3) = 2

Solution 10

Question 11
Solution 11
Question 12

Solve the following simultaneous equations:

13a - 11b = 70

11a - 13b = 74

Solution 12

Question 13

Solve the following simultaneous equations:

41x + 53y = 135

53x + 41y = 147

Solution 13

Question 14

Solve the following simultaneous equations:

65x - 33y = 97

33x - 65y = 1

Solution 14

Question 15

Solve the following simultaneous equations:

103a + 51b = 617

97a + 49b = 583

Solution 15

Question 16

Solve the following pairs of equations:

  

Solution 16

Question 17

Solve the following pairs of equations:

  

Solution 17

Question 18

Solve the following pairs of equations:

  

Solution 18

Question 19

Solve the following pairs of equations:

  

Solution 19

Question 20

Solve the following pairs of equations:

  

Solution 20

Question 21

Solve the following pairs of equations:

  

Where x ≠ 0, y ≠ 0

Solution 21

Question 22

Solve the following pairs of equations:

  

Solution 22

Question 23

Solve the following pairs of equations:

  

Solution 23

Question 24

Solve the following pairs of equations:

  

Where x + y ≠ 0 and x - y ≠ 0

Solution 24

Question 25

Solve the following pairs of equations:

  

Solution 25

 

Question 26

Solve the following pairs of equations:

  

Solution 26

Question 27

Solve the following pairs of equations:

  

Solution 27

Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32

Can the following equations hold simultaneously?

7y - 3x = 7

5y - 11x = 87

5x + 4y = 43

If yes, find the value of x and y.

Solution 32

Question 33

If the following three equations hold simultaneously for x and y, find the value of 'm'.

2x + 3y + 6 = 0

4x - 3y - 8 = 0

x + my - 1 = 0

Solution 33

Chapter 8 - Simultaneous Linear Equations Excercise Ex. 8.2

Question 1

Draw the graphs of the following linear equations:

x = 3

Solution 1

The graph of x = 3 is as follows:

 

Question 2

Draw the graphs of the following linear equations:

y + 5 = 0

Solution 2

Given equation, y + 5 = 0

i.e. y = -5

 

The graph is as follows:

 

  

Question 3

Draw the graphs of the following linear equations:

3x + 2y - 6 = 0

Solution 3

 

Question 4

Draw the graphs of the following linear equations:

5x - 5y = 8

Solution 4

 

Question 5

Draw the graph for each of the following equation: Also, find the coordinates of the points where the graph of the equation meets the coordinate axes:

  

Solution 5

 

Thus, the graph of the equation meets the X-axis at (2, 0) and Y-axis at (0, 3).

Question 6

Draw the graph for each of the following equation: Also, find the coordinates of the points where the graph of the equation meets the coordinate axes:

Solution 6

 

 

Thus, the graph of the equation meets the X-axis at (-6, 0) and Y-axis at (0, 45).

Question 7

Draw the graph of the equation 4x - 3y + 12 = 0.

Also, find the area of the triangle formed by the line drawn and the coordinate axes.

Solution 7

 

 

 

Question 8

Draw the graph of the equation

y = 5x - 4 Find graphically

a. the value of x, when y = 1

b. the value of y, when x = -2

Solution 8

 

 

From the graph, we find that

 

a. When y = 1, x = 1.

b. When x = -2, y = -14

Question 9

Use the given table and draw the graph of a straight line.

x

1

2

3

P

y

1

q

-5

7

 

Find graphically the values of 'p' and 'q'.

Solution 9

The graph is as follows:

 

 

From the graph, we find that p = -1 and q = -2.

 

Question 10

A straight line passes through the points (2, 5) and (-4, -7). Plot these points on a graph paper and draw the straight line passes through these points. If points (a, -1) and (-5, b) lie on the line drawn, find the value of a and b.

Solution 10

The graph is as follows:

 

 

From the graph, we find that a = -1 and b = -9.

Question 11
Solution 11
Question 12

Solution 12

Question 13
Solution 13
Question 14

Solution 14

Question 15

Solution 15

Question 16

Solve the following system of equations graphically:

2x = 23 - 3y

5x = 20 + 8y

Also, find the area of the triangle formed by these lines and x-axis in each graph.

Solution 16

 

 

Question 17

Solve the following system of equations graphically:

6x - 3y + 2 = 7x + 1

5x + 1 = 4x - y + 2

Also, find the area of the triangle formed by these lines and x-axis in each graph.

Solution 17

 

 

Chapter 8 - Simultaneous Linear Equations Excercise Ex. 8.3

Question 1

The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.

Solution 1

Question 2

The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.

Solution 2

Question 3

If a number is thrice the other and their sum is 68, find the numbers.

Solution 3

Question 4

The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.

Solution 4

Question 5

In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.

Solution 5

Question 6

The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.

Solution 6

Question 7

Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.

Solution 7

Question 8

If 2 is added to the numerator and denominator it becomes   and if 3 is subtracted from the numerator and denominator it becomes  Find the fraction.

Solution 8

 

Question 9

The ratio of two numbers is  . If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

Solution 9

Question 10

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes  . Find the fraction.

Solution 10

Question 11

If 1 is added to the denominator of a fraction, the fraction becomes  If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.

Solution 11

Question 12

The age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages.

Solution 12

Question 13

The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.

Solution 13

Question 14

A father's age is three times the age of his child. After 12 years, twice the age of father will be 36 more than thrice the age of his child. Find his present age.

* Question modified

Solution 14

* Question modified

Question 15

In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.

Solution 15

Question 16

In a ABC, A = x°, B = (2x - 30)°, C = y° and also, A + B = one right angle. Find the angles. Also, state the type of this triangle.

Solution 16

Question 17

A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number.

Solution 17

Question 18

Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.

Solution 18

Question 19

The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.

Solution 19

Question 20

An eraser costs Rs. 1.50 less than a sharpener. Also, the cost of 4 erasers and 3 sharpeners is Rs.29. Taking x and y as the costs (in Rs.) of an eraser and a sharpener respectively, write two equations for the above statements and find the value of x and y.

Solution 20

Question 21

A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.

Solution 21

Question 22

A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.

Solution 22

Question 23

Salman and Kirti start at the same time from two places 28 km apart. If they walk in the same direction, Salman overtakes Kirti in 28 hours but if they walk in the opposite directions, they meet in 4 hours. Find their speeds (in km/h).

Solution 23

Question 24

A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?

Solution 24

Question 25

9 pens and 5 pencils cost Rs.32, and 7 pens and 8 pencils cost Rs.29. Find the unit price for each pen and pencil.

Solution 25

Question 26

Sunil and Kafeel both have some oranges. If Sunil gives 2 oranges to Kafeel, then Kafeel will have thrice as many as Sunil. And if Kafeel gives 2 oranges to Sunil, then they will have the same numbers of oranges. How many oranges does each have?

Solution 26

Question 27

Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with  of what Samidha had in the beginning of the week. Find their pocket money.

Solution 27

Question 28

Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.

Solution 28

Question 29

A and B can build a wall in  days. If A's one day work is  of one day work of B, find in 4 how many days A and B alone can build the wall.

Solution 29

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