Mathematics - Determinant Question with Solution | TestHub

Given,

$2x-3y=\gamma +5$

$\alpha x+5y=\beta +1$

Has infinite many solutions

So, $\frac{\alpha }{2}=\frac{5}{-3}=\frac{\beta +1}{\gamma +5}$

$\Rightarrow \alpha =\frac{-10}{3}, 5\gamma +25=-3\beta -3$

$\Rightarrow 9\alpha =-30, 3\beta +5\gamma =-28$

Now, $9\alpha +3\beta +5\gamma =-58$

$\left|9\alpha +3\beta +5\gamma \right|=58$