The condition for which the pair of equations $a x+2 y=7$ and $3 x+b y=16$ represent parallel lines

Question

The condition for which the pair of equations $a x+2 y=7$ and $3 x+b y=16$ represent parallel lines is :\

Professor PC Thomas Classes · Answer

(b) : Given equation of lines are \ a x+2 y=7  ........(i) \ and $3 x+b y=16$ .........(ii)\The lines represented by (i) and (ii) are parallel, if $$ \frac{a}{3}=\frac{2}{b} 
eq \frac{7}{16} \Rightarrow a b=6 $$