MP Board Class 10 Mathematics — For what value of $k$ will

Q: For what value of $k$ will the equations $3x - y - 5 = 0$ and $6x - 2y - k = 0$ have no solution?

For no solution: $\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}$.\nHere $a1=3, b1=-1, c1=-5$ and $a2=6, b2=-2, c2=-k$. $\frac{3}{6} = \frac{-1}{-2} \neq \frac{-5}{-k} \implies \frac{1}{2} \neq \frac{5}{k} \implies k \neq 10$.\nWhen $k \neq 10$, the equations have no solution.

MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesFor what value of $k$ will the equations $3x - y - 5 = 0$ and $6x - 2y - k = 0$ have no solution?

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Step-by-Step Solution

For no solution: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.\nHere $a_1=3, b_1=-1, c_1=-5$ and $a_2=6, b_2=-2, c_2=-k$. $\frac{3}{6} = \frac{-1}{-2} \neq \frac{-5}{-k} \implies \frac{1}{2} \neq \frac{5}{k} \implies k \neq 10$.\nWhen $k \neq 10$, the equations have no solution.

Detailed Options Breakdown

Option : $k = 10$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 1: $k \neq 10$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: $k = -10$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 3: $k \neq -10$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

💡 Study Guide: This question tests core syllabus concepts from Pair of Linear Equations in Two Variables. For formulas, key summaries, and mock exam reference guides, read the full Pair of Linear Equations in Two Variables Revision Notes.

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