


Last updated at Dec. 16, 2024 by Teachoo
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 (ii) 2x + y = 5 3x + 2y = 8 2x + y = 5 3x + 2y = 8 2x + y = 5 2x + 1y – 5 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 2, b1 = 1, c1 = –5 3x + 2y = 8 3x + 2y – 8 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 3, b2 = 2, c2 = –8 a1 = 2, b1 = 1, c1 = –5 & a2 = 3, b2 = 2, c2 = –8 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 2/3 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = 1/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−5)/(−8) 𝑐1/𝑐2 = 5/8 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Solving 2x + y = 5 …(1) 3x + 2y = 8 …(2) For cross-multiplication 2x + y – 5 = 0 3x + 2y – 8 = 0 𝑥/(1×(−8) − 2 ×(−5) ) 𝑥/((−8) + 10 ) 𝑥/(2 ) = 𝑦/(3 ×(−5) − 2 × (−8) ) = 𝑦/(−15 + 16) = 𝑦/(1 ) = 1/(2 × 2 − 3 × 1 ) = 1/(4 − 3 ) = 1/1 Now, 𝒙/𝟐 = 𝟏/𝟏 x = 2 × 1 ∴ x = 2 𝒚/𝟏 = 𝟏/𝟏 y = 1 × 1 ∴ y = 1 Therefore, x = 2, y = 1 is the solution of our equation