- What is Linear equations
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- Linear equations Solutions
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- Graphical Representation of Linear equation in one and two variable
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- Steps to Draw the Given line on Cartesian plane
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- Simultaneous pair of Linear equation
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- Algebraic Solution of system of Linear equation
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- Simultaneous pair of Linear equation in Three Variable
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- Steps to solve the Linear equations

- NCERT Solutions Exercise 3.1
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- NCERT Solutions Exercise 3.2
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- NCERT Solutions Exercise 3.3,3.4,3.5
- NCERT Solutions Exercise 3.6
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- NCERT Solutions Exercise 3.7

- Problem and Solutions
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- Linear equations Problems
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- Linear equation worksheet
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- Linear equation word problems
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- Linear equations graphical problems

In this page we have *NCERT Solutions for Class 10th Maths:Linear Equations* for
Exercise 3.2. Hope you like them and do not forget to like , social_share
and comment at the end of the page.

Form the pair of linear equations in the following problems, and find their solutions graphically.

(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

i) Let number of boys =

Number of girls =

Given that total number of student is 10 so that

or

Putting

x |
10 |
0 |

y |
0 |
10 |

Given that If the number of girls is 4 more than the number of boys

So that

Putting

x |
-4 |
0 |

y |
0 |
4 |

Therefore, number of boys = 3 and number of girls = 7.

ii) Let cost of pencil = Rs

Cost of pens = Rs

5 pencils and 7 pens together cost Rs 50,

So we get

5

or

Here putting x=0, will give fractional value of y which will be difficult to drawn in graph, so we take values such that, we get integers values

Putting value of

x |
3 |
-4 |

y |
5 |
10 |

Given that 7 pencils and 5 pens together cost Rs 46

7

Putting

x |
-2 |
3 |

y |
12 |
5 |

Therefore, cost of one pencil = Rs 3 and cost of one pen = Rs 5.

On comparing the ratios

(i) 5

7

(ii) 9

18

(iii) 6

2

i) Comparing these equation with

We get

b

Hence,

Therefore, both are intersecting lines at one point.

ii)Comparing these equations with

We get

Hence,

Therefore, both lines are coincident

iii) Comparing these equations with

We get

Hence,

Therefore, both lines are parallel

On comparing the ratios

(i) 3

(ii) 2

(iii) 3/2

(iv) 5

(v) 4/3

(i) 3

Comparing these equations with

We get

Hence,

These linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

(ii) 2

Comparing these equations with

We get

Hence,

Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of linear equations is inconsistent.

(iii) 3/2

Comparing these equations with

We get

Hence,

Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

(iv) 5

Comparing these equations with

We get

Hence,

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

(v) (4/3)

Comparing these equations with

We get

Hence,

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

(ii)

(iii) 2

(iv) 2

(i)

Comparing these equations with

We get

Hence,

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

x |
0 |
5 |

y |
5 |
0 |

And, 2

This is same as Ist equation only

x |
0 |
5 |

y |
5 |
0 |

Graphical representation

(ii)

Comparing these equations with

We get

Hence,

Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of linear equations is inconsistent.

(iii) 2

Comparing these equations with

We get

Hence,

Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

2

x |
0 |
3 |

y |
6 |
0 |

And, 4

x |
0 |
1 |

y |
-2 |
0 |

From the figure, it can be observed that these lines are intersecting each other at the only one point i.e., (2,2) which is the solution for the given pair of equations.

(iv) 2

Comparing these equations with

We get

Hence,

Therefore, these linear equations are parallel to each other and thus, have no possible solution. Hence, the pair of linear equations is inconsistent.

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Let length of rectangle =

Width of the rectangle =

According to the question,

x |
0 |
-4 |

y |
4 |
0 |

x |
0 |
36 |

y |
36 |
0 |

Graphical representation

From the figure, it can be observed that these lines are intersecting each other at only point i.e., (16, 20). Therefore, the length and width of the given garden is 20 m and 16 m respectively.

Given the linear equation 2

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines

(i) Intersecting lines:

For this condition,

The second line such that it is intersecting the given line is

2

(ii) Parallel lines

For this condition,

Hence, the second line can be

6

and

(iii) Coincident lines

For coincident lines,

Hence, the second line can be

8

and

Draw the graphs of the equations

x |
0 |
-1 |

y |
1 |
0 |

3

x |
4 |
0 |

y |
0 |
6 |

From the figure, it can be observed that these lines are intersecting each other at point (2, 3) and

Given below are the links of some of the reference books for class 10 math.

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.

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