Question

Question 1 (iii)
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

Answer 1

3x - 5y = 20
6x - 10y = 40

Compare the given equations with

$a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0$.

$\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{-5}{-10}=\frac{1}{2}$
$\frac{c_1}{c_2}=\frac{-20}{-40}=\frac{1}{2}$
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other.
Thus, there are infinite solutions possible for these equations.