In obtaining the solution of the system of equations x + y + z = 7...

The given system of linear equations is:
$x + y + z = 7$
$x + 2y + 3z = 16$
$x + 3y + 4z = 22$

By Cramer's rule, the value of $y$ is given by $y = \dfrac{D_2}{D}$, where $D_2$ is the determinant obtained by replacing the second column of the coefficient matrix $D$ with the column of constant terms.

$D_2 = \begin{vmatrix} 1 \text{ and } 7 \text{ and } 1 \\ 1 \text{ and } 16 \text{ and } 3 \\ 1 \text{ and } 22 \text{ and } 4 \end{vmatrix}$

Expanding the determinant along the first row:
$D_2 = 1(16 \times 4 - 3 \times 22) - 7(1 \times 4 - 3 \times 1) + 1(1 \times 22 - 16 \times 1)$

$D_2 = 1(64 - 66) - 7(4 - 3) + 1(22 - 16)$

$D_2 = 1(-2) - 7(1) + 1(6)$

$D_2 = -2 - 7 + 6$

$D_2 = -3$

Answer: $-3$