Mathematics - Straight Lines Question with Solution | TestHub

$$\begin{array}{rl}& x+2ay+a=0\\ & x+3by+b=0\\ & x+4ay+a=0\end{array}$$ Subtracting equation (3) from (1) $$\begin{array}{rl}& -2ay=0\\ & ay=0\Rightarrow y=0\end{array}$$ Putting value of $y$ in equation (1), we get $$\begin{array}{rl}& x+0+a=0\\ & x=-a\end{array}$$ Putting value of $x$ and $y$ in equation (2), we get $$\begin{array}{rl}& -a+b=0\\ & a=b\end{array}$$ Thus, $(a,b)$ lies on a straight line