Question

For which values of a and b will the following pair of linear equations have infinitely many solutions x+2y =1 and (a-b)x +(a+b)y =a+b-2

Answer 1

Answer:

: If the a1x+b1Y+ c1 = 0,a2x+b2y+c2 = 0 system has infinitely many solutions then a1/a2 = b1/b2 = c1/c2. x + 2y = 1 , (a – b)x + (a + b)y = a + b – 2 1 / (a – b) = 2 / (a + b) = 1 / (a + b – 2) ⇒ 1 / (a – b) = 2 / (a + b) ⇒ (a + b) = 2 (a - b) ⇒ a -3b = 0 -----------(1) ⇒ 1 / (a – b) = 1 / (a + b – 2) ⇒ (a – b) = (a + b – 2) ⇒ –2b = – 2 ⇒ b = 1 b = 1 subsitute in equ (1) then ∴ a = 3 b = 1.