If the system of linear equations 7 x+11 y+α z=13 5 x+4 y+7 z=β 175 x+194 y+57 z=361 has infinitely many solutions, then α+β+2 is equal to:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Evening shift · Q4626

JEE Main 202311 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

If the system of linear equations

\begin{aligned} & 7 x+11 y+\alpha z=13 \\\\ & 5 x+4 y+7 z=\beta \\\\ & 175 x+194 y+57 z=361 \end{aligned}

has infinitely many solutions, then

\alpha+\beta+2

is equal to :

JEE Main 2023 · 11 Apr, Evening shift · Q4626

JEE Main 202311 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

If the system of linear equations

\begin{aligned} & 7 x+11 y+\alpha z=13 \\\\ & 5 x+4 y+7 z=\beta \\\\ & 175 x+194 y+57 z=361 \end{aligned}

has infinitely many solutions, then

\alpha+\beta+2

is equal to :