Question

Check whether the pair of equations $5x-4y+8=0$ and $7x+6y-9=0$ is consistent or not.

Answer 1

$5x-4y+8=0\Rightarrow a_1=5,b_1=-4,c_1=8$

$7x+6y-9=0\Rightarrow a_2=7,b_2=6,c_2=-9$

$\therefore \frac{a_1}{a_2}=\frac{5}{7}$

$\frac{-4}{6}=\frac{-2}{3}$

$\frac{c_1}{c_2}=\frac{8}{-9}$

$=\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Therefore we have a unique solution.

Our system is consistent.