Question

If $\frac{x}{5}+\frac{y}{3}=1$ and $\frac{x}{k}+\frac{y}{m}=1$, the value of $k$ is

• A. for k≠ 3m/5 a unique solution exists
• B. for k = 3ml/5 , infinitely many solutions exists.
• C. for k = 5m/3, a unique solution exists
• D. for k = 5m/3 , infinitely many solutions exist.

Answer 1

The correct option is D

for k = 5m/3 , infinitely many solutions exist.

$\frac{a_1}{a_2}=\frac{k}{5}$ $\frac{b_1}{b_2}=\frac{m}{3}$

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

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