x5+y3=1 and xk+ym=1 Choose the correct statement for k

$\frac{x}{5} + \frac{y}{3} = 1$ and $\frac{x}{k} + \frac{y}{m} = 1$ . Choose the correct statement.

for $k \neq 3 \frac{m}{5}$ a unique solution exists

for $k = 3 \frac{m}{5}$ , infinitely many solutions exists.

for $k = 5 \frac{m}{3}$ , a unique solution exists

for $k = 5 \frac{m}{3}$ , infinitely many solutions exist.

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$\frac{a_{1}}{a_{2}} = \frac{k}{5}$ $\frac{b_{1}}{b_{2}} = \frac{m}{3}$

For, unique solution, $\frac{k}{5} \neq \frac{m}{3}$ $\Rightarrow k \neq 5 \frac{m}{3}$

For, infinitely many solutions, $\frac{k}{5} = \frac{m}{3}$ $\Rightarrow k = 5 \frac{m}{3}$