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

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Question 3 Graphically, the pair of equations 6x – 3y + 10 = 0, 2x – y + 9 = 0 represents two lines which are intersecting at exactly one point (b) intersecting at exactly two points (c) coincident (d) parallel 6x – 3y + 10 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 6 , b1 = −3 , c1 = 10 2x − y + 9 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = −1 , c2 = 9 ∴ a1 = 6 , b1 = −3 , c1 = 10 & a2 = 2 , b2 = −1 , c2 = 9 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 So, we have no solution Therefore, the lines represent the linear equations are parallel So, the correct answer is (D) 𝑎1/𝑎2 = 6/2 𝑎1/𝑎2 = 3 𝑏1/𝑏2 = (−3)/(−1) 𝑏1/𝑏2 = 3 𝑐1/𝑐2 = 10/9