Ex 3.5, 1 (i) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Transcript

Ex 3.5, 1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method x – 3y – 3 = 0 3x – 9y – 2 = 0 x – 3y – 3 = 0 3x – 9y – 2 = 0 x – 3y – 3 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 1, b1 = –3, c1 = –3 3x – 9y – 2 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 3, b2 = –9, c2 = –2 a1 = 1, b1 = –3, c1 = –3 & a2 = 3, b2 = –9, c2 = –2 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 1/3 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = (−3)/(−9) 𝑏1/𝑏2 = 1/3 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−3)/(−2) Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 We have no solution.