Question 4 - MCQs from NCERT Exemplar - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Question 4 The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have: (a) a unique solution (b) exactly two solutions (c) infinitely many solutions (d) no solution x + 2y + 5 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 1 , b1 = 2 , c1 = 5 −3x − 6y + 1 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = −3 , b2 = −6 , c2 = 1 ∴ a1 = 1 , b1 = 2 , c1 = 5 & a2 = −3 , b2 = −6 , c2 = 1 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 So, we have no solution So, the correct answer is (D) 𝑎1/𝑎2 = 1/(−3) 𝑎1/𝑎2 = (−1)/3 𝑏1/𝑏2 = 2/(−6) 𝑏1/𝑏2 = (−1)/3 𝑐1/𝑐2 = 5/1