# 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 x – 3y – 3 = 0, 3x – 9y – 2 = 0 - 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

x – 3y – 3 = 0

3x – 9y – 2 = 0

#### Solution

x – 3y – 3 = 0

3x – 9y – 2 =0

a_1/a_2 = 1/3

b_1/b_2 = (-3)/-9 = 1/3  and c_1/c_2 = (-3)/-2 = 3/2

a_1/a_2 = b_1/b_2 ≠ c_1/c_2

Therefore, the given sets of lines are parallel to each other. Therefore, they will not intersect each other and thus, there will not be any solution for these equations.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 1.1 | Page 62