NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesFor what value of $k$ will the pair of equations $kx + 2y = 5$ and $3x + y = 1$ have a unique solution?
Step-by-Step Solution
For unique solution: $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.\nHere $a_1 = k, b_1 = 2$ and $a_2 = 3, b_2 = 1$. $\frac{k}{3} \neq \frac{2}{1} \implies k \neq 6$.
Detailed Options Breakdown
Option : $k = 6$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Option 1: $k \neq 6$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $k = 3$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Option 3: $k \neq 3$
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.