Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
For what value of $k$ do the equations $2x+3y=7$ and $4x+6y=k$ have infinitely many solutions?
$7$
$10$
$14$
$21$
Step-by-Step Solution
Key Concept: Apply the condition $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$.
$\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{1}{2}$. For infinitely many solutions, $\dfrac{7}{k}$ must also equal $\dfrac{1}{2}$. [0.5 Mark]
$k=14$. [0.5 Mark]
Correct Answer: $14$
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