# Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method 3x – 5y = 20, 6x – 10y = 40 - Mathematics

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method

3x – 5y = 20

6x – 10y = 40

#### Solution

3x – 5y = 20

6x – 10y = 40

a_1/a_2 = 3/6 = 1/2

b_1/b_2 = (-5)/-10 = 1/2

c_1/c_2 = (-20)/-40 = 1/2

a_1/a_2 = b_1/b_2 = c_1/c_2

Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
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Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.5 [Page 62]

#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 1.3 | Page 62

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