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JEE Math Practice Question

If the system of linear equations : $$\begin{aligned} & x+y+2 z=6 \\ & 2 x+3 y+\mathrm{az}=\mathrm{a}+1 \\ & -x-3 y+\mathrm{b} z=2 \mathrm{~b} \end{aligned}$$ where $a, b \in \mathbf{R}$, has infinitely many solutions, then $7 a+3 b$ is equal to :

  1. A.12
  2. B.9
  3. C.22
  4. D.16

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