# 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 – 7 = 0, 3x – 3y – 15 = 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 – 7 = 0

3x – 3y – 15 = 0

#### Solution

x – 3y – 7 = 0

3x – 3y – 15= 0

a_1/a_2 = 1/3

b_1/b_2 = (-3)/-3 = 1

c_1/c_2 = (-7)/-15 = 7/15

a_1/a_2 ≠ b_1/b_2

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.

By cross-multiplication,

x/(45-(21)) = y/(-21-(-15)) = 1/(-3-(-9))

x/24 = y/-6 = 1/6

x/24 = 1/6 and y/-6 = 1/6

x = 4 and y = -1

∴ x = 4, y = -1.

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 1.4 | Page 62