Solve the given two equations and select the correct option.
$I.$ $7x + 3y = 26$
$II.$ $2x + 17y = -41$

If $x$ is a solution of the equation $\sqrt{2x + 1} - \sqrt{2x - 1} = 1$ where $x \ge \frac{1}{2}$,then $\sqrt{4x^2 - 1}$ is equal to:

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$ and $\alpha + \beta$,$\alpha^2 + \beta^2$,and $\alpha^3 + \beta^3$ are in $G.P.$,where $\Delta = b^2 - 4ac$,then:

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$,where $p \neq q$,then $pq$ is equal to

The equation $(1 + 2k){x^2} + (1 - 2k)x + (1 - 2k) = 0$ is a perfect square for how many values of $k$?

The equation $\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4x - 1}$ has