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

Question

If the system of linear equations 2 x-3 y=&gamma;+5 α x +5 y =β+1, where α, β, &gamma; ∈ R has infinitely many solutions, then the value of |9 α+3 β+5 &gamma;| is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

2 x-3 y=&gamma;+5 α x+5 y=β+1 Infinite many solution (α/2)=(5/-3)=(β+1/&gamma;+5) α=(-10/3), 5 &gamma;+25=-3 β-3 9 α=-30, 3 β+5 &gamma;=-28 Now, 9 α+3 β+5 &gamma;=-58 |9 α+3 β+5 &gamma;|=58

Q. If the system of linear equations
$2 x - 3 y = γ + 5$
$αx + 5 y = β + 1$ , where $α, β, γ \in R$ has infinitely many solutions, then the value of $∣9 α + 3 β + 5 γ ∣$ is equal to

$2 x - 3 y = γ + 5$
$αx + 5 y = β + 1$
Infinite many solution
$\frac{α}{2} = \frac{5}{- 3} = \frac{β + 1}{γ + 5}$
$α = \frac{- 10}{3}, 5 γ + 25 = - 3 β - 3$
$9 α = - 30, 3 β + 5 γ = - 28$
Now, $9 α + 3 β + 5 γ = - 58$
$∣9 α + 3 β + 5 γ ∣ = 58$

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

2x−3y=γ+5 αx+5y=β+1 Infinite many solution 2α​=−35​=γ+5β+1​ α=3−10​,5γ+25=−3β−3 9α=−30,3β+5γ=−28 Now, 9α+3β+5γ=−58 ∣9α+3β+5γ∣=58

Q. If the system of linear equations
$2 x - 3 y = γ + 5$
$αx + 5 y = β + 1$ , where $α, β, γ \in R$ has infinitely many solutions, then the value of $∣9 α + 3 β + 5 γ ∣$ is equal to

$2 x - 3 y = γ + 5$
$αx + 5 y = β + 1$
Infinite many solution
$\frac{α}{2} = \frac{5}{- 3} = \frac{β + 1}{γ + 5}$
$α = \frac{- 10}{3}, 5 γ + 25 = - 3 β - 3$
$9 α = - 30, 3 β + 5 γ = - 28$
Now, $9 α + 3 β + 5 γ = - 58$
$∣9 α + 3 β + 5 γ ∣ = 58$