If the following system of linear equations

$2 x+y+z=5$

$x-y+z=3$

$x+y+a z=b$

has no solution, then :

  • [JEE MAIN 2021]
  • A

    $\mathrm{a}=-\frac{1}{3}, \mathrm{~b} \neq \frac{7}{3}$

  • B

    $a \neq \frac{1}{3}, b=\frac{7}{3}$

  • C

    $\mathrm{a} \neq-\frac{1}{3}, \mathrm{~b}=\frac{7}{3}$

  • D

    $\mathrm{a}=\frac{1}{3}, \mathrm{~b} \neq \frac{7}{3}$

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  • [IIT 2002]