Question

Sol. [Key Concept: Infinitely many solutions $\Rightarrow \ D = D_{x} = D_{y} = D_{z} = 0$; solve for $a,b$ then the line.]

$${\ D = \left| \begin{matrix} 1 & 5 & 6 \\ 2 & 3 & 4 \\ 1 & 6 & a \end{matrix} \right| = 0 }{\Rightarrow a = \frac{50}{7} }{D_{z} = 0 \Rightarrow \left| \begin{matrix} 1 & 5 & 4 \\ 2 & 3 & 7 \\ 1 & 6 & \text{ }b \end{matrix} \right| = 0 }{\Rightarrow b = \frac{29}{7} }$$$\therefore(a,b)$ lies on $x - y = 3$