Question

Find the number of solutions for $2x-3y=5$ and $4x-6y=7$ .

Answer 1

$2x-3y-5=0\Rightarrow a_1=2,b_1=-3,c_1=-5$
$4x-6y-7=0\Rightarrow a_2=4,b_2=-6,c_2=-7$

$\Rightarrow \frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2};\frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2};\frac{c_1}{c_2}=\frac{-5}{-7}=\frac{5}{7}$
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Therefore, the given system of equations are inconsistent and have no solution.
No. of solutions $=0$