The value of '$p$' for which the equations $px + 3y = p - 3$, $12x + py = p$ has infinitely many solutions is:

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Step 1: For infinitely many solutions: $\frac{p}{12} = \frac{3}{p} = \frac{p-3}{p}$. From $\frac{3}{p} = \frac{p-3}{p}$: $p = 6$. Verified: $\frac{6}{12} = \frac{3}{6} = \frac{3}{6} = \frac{1}{2}$.

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