JEE Main 2022 (Online) 26th June Evening ShiftQuestion 1
If the system of equations
$\alpha x+y+z=5$, $x+2y+3z=4$, $x+3y+5z=\beta$
has infinitely many solutions, then the ordered pair $(\alpha,\beta)$ is equal to :
Determinant
Solution
$D=\alpha-1=0\Rightarrow\alpha=1$. Eliminating with $x+2y+3z=4$, $x+3y+5z=\beta$: with $\alpha=1$ the system $x+y+z=5,\ x+2y+3z=4,\ x+3y+5z=\beta$ is consistent iff $R_3=2R_2-R_1$: $\beta=2\cdot4-5=3$. $(\alpha,\beta)=(1,3)$. Option (C).