If the system of equations x + y + z = 6 2 x + 5 y + α z = β x + 2 y + 3 z = 14 has infinitely many solutions, then α + β is equal to

Step-by-step solution

x + y + z = 6           . . . . 1 2 x + 5 y + α z = β       . . . . 2 x + 2 y + 3 z = 14           . . . 3 For infinite solution 1 1 1 2 5 α 1 2 3 = 0 ⇒ 15 - 2 α - 6 - α + 4 - 5 = 0 ⇒ 8 - α = 0 ⇒ α = 8 Also 1 1 6 2 5 β 1 2 14 = 0 ⇒ 70 - 2 β - 28 - β + 6 4 - 5 = 0 ⇒ 36 - β = 0 i.e. α = 8 ,   β = 36 ⇒ α + β = 44