Class 10 Pair of linear equations in two variables Ex 3.2

NCERT Solutions for Class 10 Maths Pair of Linear Equations in Two Variables 3.2

NCERT Solutions for Maths Chapter 3, Exercise 3.2 involve complete  answers for each question in the exercise 3.2. The solutions provide students a strategic methods  to prepare for their exam. Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.2 questions and answers helps students to perform better in exam and it will  clear doubts definitely. Students will find it extremely easy to understand the questions and learn solving the problems. NCERT Solutions for Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.2 prepared by www.mathematicsandinformationtechnology.com team in very delicate, easy and creative way. 

Question 1:

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.

Solution 1:

(i) Let the number of girls be x and the number of boys be y.

According to the question, the algebraic representation is

x + y = 10

x− y = 4

For x + y = 10,

x = 10 – y

x	5	4	6
y	5	6	4

For x − y = 4,

x	5	4	3
y	1	0	-1

x = 4 + y

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines intersect each other at point (7, 3).

Therefore, the number of girls and boys in the class are 7 and 3 respectively.

(ii)

Let the cost of 1 pencil be Rs x and the cost of 1 pen be Rs y.

According to the question, the algebraic representation is

5x + 7y = 50

7x + 5y = 46

For 5x + 7y = 50,

From the figure, it can be observed that these lines intersect each other at point (3, 5).

Therefore, the cost of a pencil and a pen are Rs 3 and Rs 5 respectively.

Question 4:

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

(i)x + y = 5, 2x + 2y = 10

(ii)x – y = 8, 3x – 3y = 16

(iii)2x + y – 6 = 0, 4x – 2y – 4 = 0

(iv)2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Solution 4:

(i)x+ y = 5

2x + 2y = 10

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines are overlapping each other.

Therefore, infinite solutions are possible for the given pair of equations.

(ii) x− y = 8

     3x − 3y = 16

Hence, the graphic representation is as follows.

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

(iv) 2x− 2y − 2 = 0

      4x − 4y − 5 = 0

Question 5:

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.

Solution 5:

Let the width of the garden be x and length be y.

According to the question,

y− x = 4 (1)

y + x = 36 (2)

y− x = 4

Question 6:

Given the linear equation 2x + 3y − 8 = 0, write another linear equations in two variables such that the geometrical representation of the pair so formed is:

(i)intersecting lines

(ii)parallel lines

(iii)coincident lines

Question 7:

Draw the graphs of the equations x − y + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Solution 7:

x− y + 1 = 0

From the figure, it can be observed that these lines are intersecting each other at point (2, 3) and x-axis at (−1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), (−1, 0), and (4, 0).