Question

Are the following pair of linear equations consistent ? justify your answer
- 3x - 4y = 12 and 4y + 3x = 12

Answer 1

- 3x - 4y = 12 and 4y + 3x = 12
Here, $\frac{a_1}{a_2}=\frac{-3}{3}=-1,\frac{b_1}{b_2}=\frac{-4}{4}=-1$ and $\frac{c_1}{c_2}=\frac{-12}{-12}=1$
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
So, the given pair of linear equations is inconsistent and has no solution.