If the system of linear equations … has infinitely many solutions, then … is equal to :

Matrices and Determinants

JEE Main 2023 · 11 Apr, Evening shift · Q4626

MathematicsMedium244×since 2002Q4626

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

MathematicsMedium244×since 2002Q4626

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 :