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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10

Question:

For what value of $k$ will the pair of equations $2x+3y=5$ and $4x+ky=10$ have infinitely many solutions?

Step-by-Step Solution

Key Concept: Apply the condition for infinitely many solutions to all three ratios.
$\dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac12$ and $\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac12$; for infinitely many solutions we also need $\dfrac{b_1}{b_2}=\dfrac12$. [1.0 Mark]

$\dfrac{3}{k}=\dfrac12 \Rightarrow k=6$. [1.0 Mark]

Correct Answer:
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