JEE Main 2022 (Online) 29th July Evening ShiftQuestion 1
If the system of equations $x+y+z=6$, $2x+5y+\alpha z=\beta$, $x+2y+3z=14$ has infinitely many solutions, then $\alpha+\beta$ is equal to
Determinant
Solution
$\begin{vmatrix}1&1&1\\2&5&\alpha\\1&2&3\end{vmatrix}=8-\alpha=0\Rightarrow\alpha=8$. $\begin{vmatrix}1&1&6\\2&5&\beta\\1&2&14\end{vmatrix}=36-\beta=0\Rightarrow\beta=36$. $\alpha+\beta=44$. Option (C).