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

2 x − 3 y = γ + 5 α x + 5 y = ( β + 1 ) } i n f i n i t e l y m a n y s o l u t i o n ∴ 2 α = − 3 5 = ( γ + 5 β + 1 ) (i) 2 α = − 3 5 = γ + 5 β + 1 α = 5 * 2 − 3 5x + 25 = -3β - 3 5 γ + 3 β = − 2 8 | 9 α + 5 γ + 3 β | = | 9 * − 1 0 3 − 2 8 | = | − 3 0 − 2 8 | = 5 8

If the system of linear equations

2x – 3y = $γ$ = 5,

aX + 5y = b + 1, where $α, β, γ \in R$ has infinitely many solutions, then the value of $| 9 α + 3 β + 5 γ |$ is equal to…………..

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Alok Kumar Singh | Contributor-Level 10

7 months ago

$\begin{matrix} 2 x - 3 y = γ + 5 & α x + 5 y = (β + 1) \end{matrix}} i n f i n i t e l y m a n y s o l u t i o n$

$∴ \frac{2}{α} = \frac{- 3}{5} = (\frac{γ + 5}{β + 1})$

(i) $\frac{2}{α} = \frac{- 3}{5} = \frac{γ + 5}{β + 1}$

$α = \frac{5 * 2}{- 3}$ 5x + 25 = -3β - 3

^{$5 γ + 3 β = - 28$}

^{$| 9 α + 5 γ + 3 β | = | 9 * \frac{- 10}{3} - 28 |$}

=^{$| - 30 - 28 | = 58$}

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