Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
For what value of $k$ will the following system of linear equations have no solution?
$3x + y = 1$ and $(2k - 1)x + (k - 1)y = 2k + 1$.
Step-by-Step Solution
Key Concept: No solution condition: $\\dfrac{3}{2k-1} = \\dfrac{1}{k-1} \<br>eq \\dfrac{1}{2k+1}$.
$\\dfrac{3}{2k-1} = \\dfrac{1}{k-1} \Rightarrow 3(k - 1) = 2k - 1 \Rightarrow 3k - 3 = 2k - 1 \Rightarrow k = 2$. [1.0 Mark]
Check $k = 2$: $\\dfrac{3}{3} = \\dfrac{1}{1} \
eq \\dfrac{1}{5}$. True! Thus $k = 2$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Cross multiplying to find $k = 2$: 1.0 Mark
Verifying inequality for no solution: 1.0 Mark
Correct Answer:
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.