Prove that if $p$ is irrational, which of the following is also an irrational number for any non-zero rational $q$ ?

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If two positive integers $a$ and $b$ are written as $a = x^{3} y^{2}$ and $b = x y^{3}$ , where $x$ and $y$ are prime numbers, what is the…
For what value of $k$ will the pair of linear equations $k x + 3 y - (k - 3) = 0$ and $12 x + k y - k = 0$ have infinitely many solutions?
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