Question

Question 1 (i)
Which of the following pairs of linear equations has a 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

Answer 1

x - 3y - 3 = 0
3x - 9y - 2 =0
$\frac{a_1}{a_2}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{-3}{-9}=\frac{1}{3}$
$\frac{c_1}{c_2}=\frac{-3}{-2}=\frac{3}{2}$
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
So, the given sets of lines are parallel to each other and they will not intersect each other.
Thus, there will not be any solution for these equations.