If the system of linear equations: x + y + 2z = 6 2x + 3y + az = a + 1 -x - 3y + bz = 2b where a, b R, has infinitely many solutions, then 7a + 3b is equal to:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q40

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

If the system of linear equations:

\begin{aligned} x + y + 2z &= 6 \\ 2x + 3y + az &= a + 1 \\ -x - 3y + bz &= 2b \end{aligned}

where

a, b \in \mathbb{R}

, has infinitely many solutions, then

7a + 3b

is equal to: