Question

Do the following pair of linear equations have no solution? Justify your answer.
2x + 4y = 3 and 12y + 6x = 6

Answer 1

Condition for no solution $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
2x + 4y = 3 and 12y + 6x = 6
$a_1=2,b_1=4,c_1=-3a_2=6,b_2=12,c_2=-6\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3},\frac{b_1}{b_2}=\frac{4}{12}=\frac{1}{3},\frac{c_1}{c_2}=\frac{-3}{-6}=\frac{1}{2}\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence, the given pair of linear equations has no solution.