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

If you love numbers & have a deep interest in statistics, then Mathematics is probably one of the scoring subject ever. A Class 9th CBSE Mathematics is one of the challenging subject one can undergo as, it involves a lot of crunching of complex numbers, geometrical formulae, diagrams & much more. Hence, to simplify the mathematical complexity, TopperLearning has framed a customise solution that involves Test preparation notes, Textbook solutions, Videos, & several other study material that help the student to memorise the concepts quickly. We have bifurcated our CBSE Class 9 Study Material (Solution) into 3 Different parts namely:

- CBSE Class 9 Practice Test includes Revision notes, Question bank & Sample Paper

- TopperLearning Classroom that includes Videos, Ask the Experts & Preparation Tips

- Text Book Solutions, etc

TopperLearning packages involves all the ingredients of CBSE Class 9 Study Material that includes Solved Question Papers, High Animated Videos, Solutions by SME (Subject Matter Expert), CBSE class 9 Preparation Tips, Update to CBSE 9th Mathematics syllabus, Practice books, Reference Materials, etc that help you to score great marks with glorious marks.

Getting a good score is now relatively easy if you prefer TopperLearning solutions for CBSE Class 9th Mathematics subject. By purchasing our package, you will be accessed to guaranteed success in your examination!

## Chapter 7 - Linear Equations in Two Variables Exercise 7.33

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

(a) 3

(b) 4

(c) 5

(d) 6

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).

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

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).

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)

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).

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

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

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).

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

(a) a line

(b) a point

(c) infinitely many lines

(d) two lines

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).

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

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).

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

(a) 1

(b) 2

(c) 3

(d) 4

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).

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

(a) 1

(b) 2

(c) 3

(d) 5

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

= 2 - (-3)

= 2 + 3

= 5

Hence, correct option is (d).

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

(a) 2

(b) 4

(c) 3

(d) 1

The distance between given two graphs

= 3 - (-1)

= 3 + 1

= 4

Hence, correct option is (b).

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

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

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

If x = 1 and y = 6 is solution of the equation 8x - ay + a^{2}= 0, find the value of a.

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

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

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

**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).**

**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).**

**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**** **

**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**** **

**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**

**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.**

**Draw the graph of y = |x|.**

**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|:**

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

**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:**

**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.**

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

**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**

**y = 3Point A represents 3 on number line. On Cartesian plane, equation represents all points on x axis for which y = 3**

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

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

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

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

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

**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)**

**(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**

## CBSE Class 9 Maths Homework Help

Clear all your doubts instantly at our “Ask Doubt” section. Get expert help and guidance at your comfort. To know the syllabus in detail, click here.

NCERT Textbooks are the rich stimulant for those students who want to score better in the CBSE examinations. By solving our papers the students have achieved a better and higher result. One of the primary objectives of creating ncert solution for class 9 is that the student gets access to an easy solution; which acts as a strong catalyst in improving the marks. We usually focus that the students don’t find any difficulty in understanding the concepts and can memorize them easily.

#### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change