JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1
If the system of linear equations :
$x+y+z=6$,
$x+2y+5z=10$,
$2x+3y+\lambda z=\mu$
has infinitely many solutions, then the value of $\lambda+\mu$ equals :
Determinant
Solution
Subtract: $R_2-R_1$: $y+4z=4$; $R_3-2R_1$: $y+(\lambda-2)z=\mu-12$. Infinite solutions need the last two identical: $\lambda-2=4\Rightarrow\lambda=6$, $\mu-12=4\Rightarrow\mu=16$. $\lambda+\mu=22$. Option (C).