Pair Of Linear Equations In Two Variables Ex 3.2 Solution

Pair of Linear Equations in Two Variables Ex 3.2 introduces the method of solving a pair of linear equations in two variables algebraically. In this exercise, students apply the method of substitution, where one equation is solved for one variable and substituted into the other. This forms the foundation for solving real-life mathematical problems using linear equations.

Pair of Linear Equations in Two Variables Ex 3.2 Textbook solutions

Question 1.| Pair of Linear Equations in Two Variables Ex 3.2
Form the pair of linear equations of 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 ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and that of one pen.
Solution:

NCERT Solutions for Class 10 Maths Chapter 3 Pdf Pair Of Linear Equations In Two Variables Ex 3.2 Q1

NCERT Solutions for Class 10 Maths Chapter 3 Pdf Pair Of Linear Equations In Two Variables Ex 3.2 Q1.1

NCERT Solutions for Class 10 Maths Chapter 3 Pdf Pair Of Linear Equations In Two Variables Ex 3.2 Q1.2

Question 2.| Pair of Linear Equations in Two Variables Ex 3.2
On comparing the ratios a1/a2, b1/b2
and c1/c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) 5x – 4y + 8 = 0, 7x + 6y – 9 = 0
(ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0
(iii) 6x – 3y + 10 = 0, 2x -y + 9 = 0
Solution:

Ex 3.2 Class 10 Maths Question 3.
On comparing the ratios a1a2, b1b2
and c1c2, find out whether the following pairs of linear equations are consistent, or inconsistent:
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Solution:

Ex 3.2 Class 10 Maths 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:

Ex 3.2 Class 10 Maths 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 graphically.
Solution:

Ex 3.2 Class 10 Maths Question 6.
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines

SOLUTION:

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: