Solve the given two equations and select the correct answer from the given options.
$I. \quad 4x + 7y = 209$
$II. \quad 12x - 14y = -38$

Solve the given two equations and select the correct answer from the given options.
$I. x^{2}-19x+84=0$
$II. y^{2}-25y+156=0$

Let $\alpha$ and $\beta$ be the roots of the equation $x^{2}-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 6x + \lambda = 0$ and $3\alpha + 2\beta = -20$,then $\lambda = $

If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^{2} + bx + c = 0$,the value of $\alpha^{3} + \beta^{3}$ is

If $4a - \frac{4}{a} + 3 = 0$,then the value of $a^{3} - \frac{1}{a^{3}} + 3$ is equal to?