Solve the given two equations and select the correct option.
$I.$ $7x - 3y = 13$
$II.$ $5x + 4y = 40$

If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

If $2 + i\sqrt{3}$ is a root of the equation $x^2 + px + q = 0$,where $p$ and $q$ are real,then $(p, q) = $

The value of $x$ in the equation $\left(x+\frac{1}{x}\right)^{2}-\frac{3}{2}\left(x-\frac{1}{x}\right)=4$ is

If the roots of the equation $5x^2 - 7x + k = 0$ are reciprocals of each other,then the value of $k$ is:

Let $a \ne b, c \ne 0$. If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root,then:
Statement $-1$: The equation of the other roots is $x^2 + cx + ab = 0$.
Statement $-2$: $a + b + c = 0$.