If the system of linear equations 2 x - 3 y = γ + 5 α x + 5 y = β + 1 , where α , β , γ ∈ R has infinitely many solutions, then the value of 9 α + 3 β + 5 γ is equal to

Step-by-step solution

Given, 2 x - 3 y = γ + 5 α x + 5 y = β + 1 Has infinite many solutions So, α 2 = 5 - 3 = β + 1 γ + 5 ⇒ α = - 10 3 ,    5 γ + 25 = - 3 β - 3 ⇒ 9 α = - 30 ,    3 β + 5 γ = - 28 Now, 9 α + 3 β + 5 γ = - 58 9 α + 3 β + 5 γ = 58