Question

Question 3 (ii)
Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5}x-y=\frac{1}{2}and\frac{1}{5}x-3y=\frac{1}{6}$

Answer 1

$\frac{3}{5}x-y=\frac{1}{2}and\frac{1}{5}x-3y=\frac{1}{6}Here,a_1=\frac{3}{5},b_1=-1,c_1=-\frac{1}{2}and{a}_2=\frac{1}{5},b_2=-3,c_2=-\frac{1}{6}Now,\frac{a_1}{a_2}=\frac{3}{1},\frac{b_1}{b_2}=\frac{-1}{-3}=\frac{1}{3},\frac{c_1}{c_2}=\frac{3}{1}$
$\because$ $\frac{a_1}{a_2}$ $\ne$ $\frac{b_1}{b_2}$
The given pair of linear equations has a unique solution.

Thus, the system of equations is consistent.