Solve the following pair of linear equations by the method of substitution: $x + y = 7$ and $5x + 12y = 7$.

Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$	$a.$ $x = 3, y = 2$
$2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$	$b.$ $x = 3, y = 1$
$3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$	$c.$ $x = 2, y = 1$
$4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$	$d.$ $x = 1, y = 2$

For which values of $p$ and $q$ will the following pair of linear equations have infinitely many solutions?
$4x + 5y = 2$
$(2p + 7q)x + (p + 8q)y = 2q - p + 1$

For which value$(s)$ of $\lambda$,do the pair of linear equations $\lambda x + y = \lambda^2$ and $x + \lambda y = 1$ have:
$(i)$ no solution?
$(ii)$ infinitely many solutions?
$(iii)$ a unique solution?

For what value of $k,$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?

The graph of the equation $\ldots \ldots \ldots \ldots$ is parallel to the $X$-axis.