#### Chapters

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equation In Two Variables

Chapter 5: Introduction To Euclid's Geometry

Chapter 6: Lines & Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Areas of Parallelograms & Triangles

Chapter 10: Circles

Chapter 11: Construction

Chapter 12: Heron's Formula

Chapter 13: Surface Area & Volumes

Chapter 14: Statistics & Probability

## Chapter 4: Linear Equation In Two Variables

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

#### Choose the correct alternative:

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

A unique solution

Two solutions

Infinitely many solutions

No solution

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

Natural numbers

Positive real numbers

Real numbers

Rational numbers

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

4

6

5

2

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)

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

(2, 0)

(0, 3)

(3, 0)

(0, 2)

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

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

(x, y)

(0, y)

(x, 0)

(x, x)

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

(a, a)

(0, a)

(a, 0)

(a, – a)

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

x = 0

y = 0

x + y = 0

x = y

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.

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

x + 2 y = 7

5x + 2y = 7

x + y = 7

5x + y = 7

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

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

1

^{st}quadrant2

^{nd}quadrant3

^{rd }quadrant4

^{th}quadrant

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)

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)`

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

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

Only one

Two

Infinitely many

Three

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

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

x = a

y = – a

y = x

x + y = 0

### 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:

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

True

False

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

True

False

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

True

False

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

True

False

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

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

True

False

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

True

False

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

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

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

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.

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

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

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

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

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

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

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

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

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?

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

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.

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

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

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

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?

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?

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?

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?

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.

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.

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

## 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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