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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
Assertion (A): The pair of equations $2x+3y=5$ and $4x+6y=10$ has infinitely many solutions. Reason (R): For this pair, $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac12$.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A. Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A. Assertion (A) is true, but Reason (R) is false. Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: Direct application of the infinite-solutions condition.
$\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{5}{10}=\dfrac12$ — all three ratios are equal, so A is true. [0.5 Mark]
R correctly states this exact equality of ratios, which is precisely the condition for infinitely many solutions, so R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
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