Find the values of $k$ for which the system of equations $x + 2y = 3$ and $5x + ky + 7 = 0$ has no solution.
Step-by-Step Solution
Key Concept: No solution condition: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} <br>eq \dfrac{c_1}{c_2}$.
Rewrite equations: $x + 2y - 3 = 0$ and $5x + ky + 7 = 0$.
$a_1=1, b_1=2, c_1=-3$ and $a_2=5, b_2=k, c_2=7$. [0.5 Mark]
For no solution: $\dfrac{1}{5} = \dfrac{2}{k}
eq \dfrac{-3}{7}$. [0.5 Mark]
From $\dfrac{1}{5} = \dfrac{2}{k} \Rightarrow k = 10$. Also $\dfrac{2}{10} = \dfrac{1}{5}
eq -\dfrac{3}{7}$ holds true. Thus $k = 10$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up ratio condition for no solution: 1.0 Mark
Solving for $k = 10$ and verifying inequality: 1.0 Mark
Correct Answer: