Question

2x + 3y=7, 2ax+3(alpha + beta )y =28. Find alpha and beta

Answer 1

Sol : Given pair of equations 2x + 3y = 7 and 2αx + (α + β )y = 28 If pair of equations have infinite many solutions then a1 / a2 = b1 / b2 = c1 / c2 . a1 = 2  a2 = 2α ,  b1 = 3 ,b2 = (α + β ) ,c1 = 7 ,c2 = 28 1 / α = 3 / (α + β ) = 7 / 28 1 / α = 7 / 28  ⇒ α = 4  α  = 4 ---------(1)  and 3 / (α + β ) = 7 / 28   (α + β ) = 12 ---------(2) from Equations (1) and (2) we get β = 8