# NCERT solutions for Mathematics Exemplar Class 9 chapter 4 - Linear Equation In Two Variables [Latest edition]

## Chapter 4: Linear Equation In Two Variables

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4
Exercise 4.1 [Pages 34 - 35]

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 4 Linear Equation In Two Variables Exercise 4.1 [Pages 34 - 35]

#### Choose the correct alternative:

Exercise 4.1 | Q 1 | Page 34

The linear equation 2x – 5y = 7 has ______.

• A unique solution

• Two solutions

• Infinitely many solutions

• No solution

Exercise 4.1 | Q 2 | Page 34

The equation 2x + 5y = 7 has a unique solution, if x and y are ______.

• Natural numbers

• Positive real numbers

• Real numbers

• Rational numbers

Exercise 4.1 | Q 3 | Page 34

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is ______.

• 4

• 6

• 5

• 2

Exercise 4.1 | Q 4 | Page 34

Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form ______.

• (- 9/2, m)

• (n, - 9/2)

• (0, - 9/2)

• (– 9, 0)

Exercise 4.1 | Q 5 | Page 34

The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point ______.

• (2, 0)

• (0, 3)

• (3, 0)

• (0, 2)

Exercise 4.1 | Q 6 | Page 34

The equation x = 7, in two variables, can be written as ______.

• 1 . x + 1 . y = 7

• 1. x + 0. y = 7

• 0 . x + 1 . y = 7

• 0 . x + 0 . y = 7

Exercise 4.1 | Q 7 | Page 34

Any point on the X-axis is of the form ______.

• (x, y)

• (0, y)

• (x, 0)

• (x, x)

Exercise 4.1 | Q 8 | Page 34

Any point on the line y = x is of the form ______.

• (a, a)

• (0, a)

• (a, 0)

• (a, – a)

Exercise 4.1 | Q 9 | Page 35

The equation of x-axis is of the form ______.

• x = 0

• y = 0

• x + y = 0

• x = y

Exercise 4.1 | Q 10 | Page 35

The graph of y = 6 is a line ______.

• Parallel to x-axis at a distance 6 units from the origin

• Pparallel to y-axis at a distance 6 units from the origin

• Making an intercept 6 on the x-axis.

• Making an intercept 6 on both the axes.

Exercise 4.1 | Q 11 | Page 35

x = 5, y = 2 is a solution of the linear equation ______.

• x + 2 y = 7

• 5x + 2y = 7

• x + y = 7

• 5x + y = 7

Exercise 4.1 | Q 12 | Page 35

If a linear equation has solutions (–2, 2), (0, 0) and (2, – 2), then it is of the form ______.

• y – x = 0

• x + y = 0

• –2x + y = 0

• –x + 2y = 0

Exercise 4.1 | Q 13 | Page 35

The positive solutions of the equation ax + by + c = 0 always lie in the ______.

Exercise 4.1 | Q 14 | Page 35

The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point ______.

• (0, 2)

• (2, 0)

• (3, 0)

• (0, 3)

Exercise 4.1 | Q 15 | Page 35

The graph of the linear equation y = x passes through the point ______.

• (3/2, (-3)/2)

• (0, 3/2)

• (1, 1)

• ((-1)/2, 1/2)

Exercise 4.1 | Q 16 | Page 35

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation: ______.

• Changes

• Remains the same

• Changes in case of multiplication only

• Changes in case of division only

Exercise 4.1 | Q 17 | Page 35

How many linear equations in x and y can be satisfied by x = 1 and y = 2?

• Only one

• Two

• Infinitely many

• Three

Exercise 4.1 | Q 18 | Page 35

The point of the form (a, a) always lies on: ______.

• X-axis

• Y-axis

• On the line y = x

• On the line x + y = 0

Exercise 4.1 | Q 19 | Page 35

The point of the form (a, – a) always lies on the line ______.

• x = a

• y = – a

• y = x

• x + y = 0

Exercise 4.2 [Page 37]

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 4 Linear Equation In Two Variables Exercise 4.2 [Page 37]

#### State whether the following statement is True or False:

Exercise 4.2 | Q 1.(i) | Page 37

The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12

• True

• False

Exercise 4.2 | Q 1.(ii) | Page 37

The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

• True

• False

Exercise 4.2 | Q 1.(iii) | Page 37

The graph given below represents the linear equation x + y = 0.

• True

• False

Exercise 4.2 | Q 1.(iv) | Page 37

The graph given below represents the linear equation x = 3 (see figure).

• True

• False

Exercise 4.2 | Q 1.(v) | Page 37

The coordinates of points in the table:

 x 0 1 2 3 4 y 2 3 4 –5 6

represent some of the solutions of the equation x – y + 2 = 0.

• True

• False

Exercise 4.2 | Q 1.(vi) | Page 37

Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

• True

• False

Exercise 4.2 | Q 1.(vii) | Page 37

The graph of every linear equation in two variables need not be a line.

• True

• False

Exercise 4.3 [Pages 38 - 39]

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 4 Linear Equation In Two Variables Exercise 4.3 [Pages 38 - 39]

Exercise 4.3 | Q 1 | Page 38

Draw the graphs of linear equations y = x and y = – x on the same cartesian plane. What do you observe?

Exercise 4.3 | Q 2 | Page 39

Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1/2 times its abscissa.

Exercise 4.3 | Q 3 | Page 39

Draw the graph of the equation represented by a straight line which is parallel to the x-axis and at a distance 3 units below it.

Exercise 4.3 | Q 4 | Page 39

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Exercise 4.3 | Q 5 | Page 39

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

Exercise 4.3 | Q 6 | Page 39

If the point (3, 4) lies on the graph of 3y = ax + 7, then find the value of a.

Exercise 4.3 | Q 7.(i) | Page 39

How many solution(s) of the equation 2x + 1 = x – 3 are there on the number line

Exercise 4.3 | Q 7.(ii) | Page 39

How many solution(s) of the equation 2x + 1 = x – 3 are there on the cartesian plane

Exercise 4.3 | Q 8.(i) | Page 39

Find the solution of the linear equation x + 2y = 8 which represents a point on x-axis

Exercise 4.3 | Q 8.(ii) | Page 39

Find the solution of the linear equation x + 2y = 8 which represents a point on y-axis

Exercise 4.3 | Q 9 | Page 39

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.

Exercise 4.3 | Q 10 | Page 39

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5?

Exercise 4.4 [Pages 41 - 42]

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 4 Linear Equation In Two Variables Exercise 4.4 [Pages 41 - 42]

Exercise 4.4 | Q 1 | Page 41

Show that the points A(1, 2), B(– 1, – 16) and C(0, – 7) lie on the graph of the linear equation y = 9x – 7.

Exercise 4.4 | Q 2.(i) | Page 41

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation:

 x 6 – 6 y –2 6

Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation cuts the x-axis

Exercise 4.4 | Q 2.(ii) | Page 41

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation:

 x 6 – 6 y –2 6

Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation cuts the y-axis

Exercise 4.4 | Q 3 | Page 41

Draw the graph of the linear equation 3x + 4y = 6. At what points, the graph cuts the x-axis and the y-axis.

Exercise 4.4 | Q 4.(i) | Page 42

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = (5F - 160)/9. If the temperature is 86°F, what is the temperature in Celsius?

Exercise 4.4 | Q 4.(ii) | Page 42

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = (5F - 160)/9. If the temperature is 35°C, what is the temperature in Fahrenheit?

Exercise 4.4 | Q 4.(iii) | Page 42

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = (5F - 160)/9. If the temperature is 0°C what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

Exercise 4.4 | Q 4.(iv) | Page 42

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = (5F - 160)/9. What is the numerical value of the temperature which is same in both the scales?

Exercise 4.4 | Q 5.(i) | Page 42

If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation y = 9/5 (x - 273) + 32. Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.

Exercise 4.4 | Q 5.(ii) | Page 42

If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation y = 9/5 (x - 273) + 32. If the temperature is 158°F, then find the temperature in Kelvin.

Exercise 4.4 | Q 6 | Page 42

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is (i) 5 m/sec-2 (ii) 6 m/sec-2.

## Chapter 4: Linear Equation In Two Variables

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4

## NCERT solutions for Mathematics Exemplar Class 9 chapter 4 - Linear Equation In Two Variables

NCERT solutions for Mathematics Exemplar Class 9 chapter 4 (Linear Equation In Two Variables) 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 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 9 chapter 4 Linear Equation In Two Variables are Solution of a Linear Equation, Graph of a Linear Equation in Two Variables, Linear Equation in Two Variables, Equations of Lines Parallel to the X-axis and Y-axis, Linear Equation in One Variable.

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