RD SHARMA Solutions for Class 9 Maths Chapter 7 - Linear Equations in Two Variables

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Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.1

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.2

Question 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 6

If x = 1 and y = 6 is solution of the equation 8x - ay + a2= 0, find the value of a.

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7(i)

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the follwoing equation: 5x - 2y = 10

Solution 7(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7(ii)

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation: -4x + 3y = 12

Solution 7(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 7(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.3

Question 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(v)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(v)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(vi)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(vi)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(vii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(vii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(viii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(viii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 4

Plot the points (3,5) and (-1,3) on a graph paper and verify that the straight line passing through these points also passes through the point (1,4).

Solution 4

The given points on the graph:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

It is dear from the graph, the straight line passing through these points also passes through the point (1,4).

Question 5

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x

(ii) x + y = 0

(iii) y = 2x

(iv) 2 + 3y = 7x

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 6

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x + 2

(ii) y = x - 2

(iii) y = -x + 2

(iv) x + 2y = 6

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 8

Draw the graph of the equation 2x + 3y = 12. Find the graph, find the coordinates of the point.

(i) whose y-coordinate is 3.

(ii) whose x-coordinate is -3

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 9(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 9(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 9(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 9(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 9(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 9(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two VariablesRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 9(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 9(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 12

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten's digit of the number are x and y respectively, then write the linear equation representing the above statement.

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 15

Draw the graph of y = |x|.

Solution 15

We have,

y = |X|                               ...(i)

Putting x = 0, we get y = 0

Putting x = 2, we get y = 2

Putting x = -2, we get y = 2

Thus, we have the following table for the points on graph of |x|.

x 0 2 -2
y 0 2 2



The graph of the equation y = |x|:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 16

Draw the graph of y = |x| + 2.

Solution 16

We have,

y = |x| + 2                                                  ...(i)

Putting x = 0, we get y = 2

Putting x = 1, we get y = 3

Putting x = -1, we get y = 3

Thus, we have the following table for the points on graph of |x| + 2:

x 0 1 -1
y 2 3 3



The graph of the equation y = |x| + 2:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 20

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years form now, I shall be three times as old as you will be". If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.4

Question 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

y + 3 = 0

y = -3

Point A represents -3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = -3

Question 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

y = 3

Point A represents 3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = 3

Question 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(iv)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 1(v)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1(v)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2(i)

Give the geometrical representation of 2x + 13 = 0 as an equation in

One variable

Solution 2(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2(ii)

Give the geometrical representation of 2x + 13 = 0 as an equation in

Two variables

Solution 2(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3(i)

Solve the equation 3x + 2 = x - 8, and represent the solution on (i) the number line.

Solution 3(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3(ii)

Solve the equation 3x + 2 = x - 8, and represent the solution on (ii) the Cartesian plane.

Solution 3(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

On Cartesian plane, equation represents all points on y axis for which x = -5

Question 4

Write the equation of the line that is parallel to x-axis and passing through the point

(i) (0,3)

(ii) (0,-4)

(iii) (2,-5)

(iv) (3,4)

Solution 4

(i) The equation of the line that is parallel to x-axis and passing through the point (0,3) is y = 3

(ii) The equation of the line that is parallel to x-axis and passing through the point (0,-4) is y = -4

(iii) The equation of the line that is parallel to x-axis and passing through the point (2,-5) is y = -5

(iv) The equation of the line that is parallel to x-axis and passing through the point (3, 4) is y = 4

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise 7.33

Question 1

If (4, 19) is a solution of the equation y = ax + 3, then a = 

(a) 3

(b) 4

(c) 5

(d) 6

Solution 1

y = ax + 3

If (4, 19) is its solution, then it must satisfy the equation.

Thus, we have

19 = a × 4 + 3

i.e. 4a = 16

i.e. a = 4

Hence, correct option is (b).

Question 2

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

(a) 3

(b) 1

(c) 2

(d) 4

Solution 2

3x + y = 10

If (a, 4) lies on its graph, then it must satisfy the equation.

Thus, we have

3(a) + 4 = 10

i.e. 3a = 6

i.e. a = 2

Hence, correct option is (c).

Question 3

The graph of the linear equation 2x - y = 4 cuts x-axis at

(a) (2, 0)

(b) (-2, 0)

(c) (0, -4)

(d) (0, 4)

Solution 3

On x-axis, the y-co-ordinate is always 0.

So, 2x - y = 4 will cut the x-axis where y = 0

i.e. 2x = 4

i.e. x = 2

Thus, 2x - y = 4 will cut the x-axis at (2, 0).

Hence, correct option is (a).

Question 4

How many linear equations are satisfied by x = 2 and y = -3?

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

Solution 4

From Point (2, -3) there are infinitely many lines passing in every-direction.

So (2, -3) is satisfied with infinite linear equations.

Hence, correct option is (d).

Question 5

The equation x - 2 = 0 on number line is represented by

(a) a line

(b) a point

(c) infinitely many lines

(d) two lines

Solution 5

Given equation is x – 2 = 0.

If this is treated as an equation in one variable x only, then it has the unique solution x = 2, which is a point on the number line. 

However, when treated as an equation in two variables, it can be expressed as x - 2 = 0.

So as, an equation in two variables, x – 2 = 0 is represented by a single line parallel to y-axis at a distance of 2 units.

Hence, correct option is (a).

Question 6

x = 2, y = -1 is a solution of the linear equation

(a) x + 2y = 0

(b) x + 2y = 4

(c) 2x + y = 0

(d) 2x + y = 5

Solution 6

Substituting x = 2 and y = -1 in the following equations:

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 = R.H.S.

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 ≠ 4 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 0 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 5 ≠ R.H.S.

Hence, correct option is (a).

Question 7

If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =

(a) 1

(b) 2

(c) 3

(d) 4

Solution 7

If (2k - 1, k) is solution of equation 10x - 9y = 12, then it must satisfy this equation.

Thus, we have

10(2k - 1) - 9k = 12

20k - 10 - 9k = 12

11k = 22

k = 2

Hence, correct option is (b).

Question 8

The distance between the graph of the equations x = -3 and x = 2 is

(a) 1

(b) 2

(c) 3

(d) 5

Solution 8

The distance between the graph of the equations x = -3 and x = 2

= 2 - (-3)

= 2 + 3

= 5

Hence, correct option is (d).

Question 9

The distance between the graphs of the equations y = -1 and y = 3 is

(a) 2

(b) 4

(c) 3

(d) 1

Solution 9

The distance between given two graphs

= 3 - (-1)

= 3 + 1

= 4

Hence, correct option is (b).

Question 10

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length

(a) 4 units

(b) 3 units

(c) 5 units

(d) none of these

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables