For what value of $p$ does the pair of linear equations $4 x + p y + 8 = 0$ and $2 x + 2 y + 2 = 0$ have a unique solution?

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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?
If $α$ and $β$ are the zeroes of the quadratic polynomial $p (x) = 2 x^{2} - 5 x + 7$ , what is the value of $α^{- 1} + β^{- 1}$ ?
Which of the following numbers is an irrational number?
The roots of the quadratic equation $3 x^{2} - 6 x + 2 = 0$ are:
If the lines given by $3 x + 2 k y = 2$ and $2 x + 5 y + 1 = 0$ are parallel, what is the value of $k$ ?

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