RD SHARMA SOLUTION CHAPTER – 7 Linear Equations in Two Variables | CLASS 9TH MATHEMATICS-EDUGROWN

Chapter 7 Linear Equations in Two Variables Exercise Ex. 7.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Chapter 7 Linear Equations in Two Variables Exercise Ex. 7.2

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

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

Question 7(i)

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the follwoing equation: 5x – 2y = 10Solution 7(i)

Question 7(ii)

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation: -4x + 3y = 12Solution 7(ii)

Question 7(iii)

Solution 7(iii)

Chapter 7 Linear Equations in Two Variables Exercise Ex. 7.3

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 1(vi)

Solution 1(vi)

Question 1(vii)

Solution 1(vii)

Question 1(viii)

Solution 1(viii)

Question 2

Solution 2

Question 3

Solution 3

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:



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

 Solution 5

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

 Solution 6

Question 7

Solution 7

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 -3Solution 8

Question 9(i)

Solution 9(i)

Question 9(ii)

Solution 9(ii)

Question 9(iii)

Solution 9(iii)

Question 9(iv)

Solution 9(iv)

Question 10

Solution 10

Question 11

Solution 11

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

Question 13

Solution 13

Question 14

Solution 14

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|:

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:

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

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

Question 21

Solution 21

Chapter 7 Linear Equations in Two Variables Exercise Ex. 7.4

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

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 = -3Question 1(iii)

Solution 1(iii)

y = 3

Point A represents 3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = 3Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 2(i)

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

One variableSolution 2(i)

Question 2(ii)

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

Two variablesSolution 2(ii)

Question 3(i)

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

Question 3(ii)

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

On Cartesian plane, equation represents all points on y axis for which x = -5Question 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 = 4Question 5

Solution 5