Question 10 - MCQs from NCERT Exemplar - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Question 10 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value cx − y − 2 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = c , b1 = −1 , c1 = −2 6x − 2y − 3 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 6 , b2 = −2, c2 = −3 Therefore, a1 = c , b1 = −1 , c1 = −2 & a2 = 6 , b2 = −2, c2 = −3 𝑎1/𝑎2 = 𝑐/6 𝑏1/𝑏2 = (−1)/(−2) 𝑏1/𝑏2 = 1/2 𝑐1/𝑐2 = (−2)/(−3) 𝑐1/𝑐2 = 2/3 Since the equations have infinitely many solutions 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 𝑐/6=1/2=2/3 This is never true as 1/2≠ 2/3 ∴ There is no possible value of c So, the correct answer is (D)