Question

how many solution have the pair of linear equation 2x+3y-9=0and 4x+6y-18=o​

Answer 1

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{2}{4} = \frac{3}{6} = \frac{ - 9}{ - 18} \\ \frac{1}{2} = \frac{1}{2} = \frac{1}{2} \\ many \: solutions \\ coincident \: line \\ coincident$

Answer 2

$\Huge{\textbf{\textsf{{\red{Ans}}{\green{wer}}{\color{pink}{:}}}}}$

$\huge\mathbb\red{MANY\:\:SOLUTION}$

$\huge\mathbb\red{Explanation \:\implies }$

Conditions for having many solution :

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \implies \frac{2}{4} = \frac{3}{6} = \frac{ - 9}{ - 18} \\ \implies \frac{1}{2} = \frac{1}{2} = \frac{1}{2}$

Actually both equation are same.