JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1
If the system of equations
$x+5y+6z=4$,
$2x+3y+4z=7$,
$x+6y+az=b$
has infinitely many solutions, then the point $(a,b)$ lies on the line
Determinant
Solution
Coefficient det $=1(3a-24)-5(2a-4)+6(9)=50-7a=0\Rightarrow a=\frac{50}{7}$. Consistency: $\begin{vmatrix}1&5&4\\2&3&7\\1&6&b\end{vmatrix}=0\Rightarrow b=\frac{29}{7}$ (rank of coefficient matrix is 2, so infinitely many solutions). $a-b=\frac{21}{7}=3\Rightarrow x-y=3$. Option (B).