QJEEM22Madb38: JEE Main 2022 Mathematics - Class 12 JEEM22Madb38 Solution: If the system of linear equations 2 x − 3 y = γ + 5 , α x + 5 y …

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QJEEM22Madb38: JEE Main 2022 Mathematics - Class 12 JEEM22Madb38 Solution: If the system of linear equations 2 x − 3 y = γ + 5 , α x + 5 y …

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

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Accepted Answer

If 2x $-$ 3y = $γ$ + 5 and $α$ x + 5y = $β$ + 1 have infinitely many solutions then

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

$\Rightarrow α = - \frac{10}{3}$ and $3 β + 5 γ = - 28$

So $| 9 α + 3 β + 5 γ | = | - 30 - 28 | = 58$

QJEEM22Madb38: JEE Main 2022 Mathematics - Class 12 JEEM22Madb38 Solution: If the system of linear equations 2 x − 3 y = γ + 5 , α x + 5 y …

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