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Ex 3.2, 3 - On comparing ratios, find if consistent or inconsistent

Ex 3.2, 3 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2

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Ex 3.2, 3 On comparing the ratios 𝑎1/𝑎2 , 𝑏1/𝑏2 & 𝑐1/𝑐2 , find out whether the following pair of linear equations are consistent, or inconsistent. 3x + 2y = 5 ; 2x – 3y = 7 3x + 2y – 5 = 0 2x – 3y – 7 = 0 3x + 2y – 5 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3 , b1 = 2 , c1 = –5 2x – 3y – 7 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = –3 , c2 = –7 a1 = 3 , b1 = 2 , c1 = –5 & a2 = 2 , b2 = –3 , c2 = –7 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 3/2 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = 2/(−3) 𝑏1/𝑏2 = (−2)/3 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−5)/(−7) 𝑐1/𝑐2 = 5/7 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Therefore, our system is consistent.

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