Solve the following pairs of equations using the comparison method: (ii) 2x - 3y = 8 and (x+y)/(x-y) = 7/3. (v) x + y = 11 and y + 2 = (1/8)(10y + x).

(ii)

$\begin{cases} 2x - 3y = 8 \\ x + y = 7 \end{cases}$

Step 1: Solve the second equation for $x$.
$x + y = 7$
$x = 7 - y$

Step 2: Substitute $x = 7 - y$ into the first equation.
$2(7 - y) - 3y = 8$
$14 - 2y - 3y = 8$
$14 - 5y = 8$

Step 3: Solve for $y$.
$-5y = 8 - 14$
$-5y = -6$
$y = \dfrac{-6}{-5} = \dfrac{6}{5}$

Step 4: Substitute $y = \dfrac{6}{5}$ into $x = 7 - y$.
$x = 7 - \dfrac{6}{5} = \dfrac{35}{5} - \dfrac{6}{5} = \dfrac{29}{5}$

$x = \dfrac{29}{5}$, $y = \dfrac{6}{5}$
x = \frac{29{5},\ y = \frac{6}{5}}

(iii)

$\begin{cases} x + y = 7 \\ x - y = 3 \end{cases}$

Step 1: Add the two equations.
$(x + y) + (x - y) = 7 + 3$
$2x = 10$
$x = \dfrac{10}{2} = 5$

Step 2: Substitute $x = 5$ into the first equation.
$5 + y = 7$
$y = 7 - 5 = 2$

$x = 5$, $y = 2$
x = 5,\ y = 2

(iv)

$\begin{cases} x + y = 11 \\ y + 2 = \dfrac{10y + x}{8} \end{cases}$

Step 1: Multiply the second equation by 8 to eliminate the denominator.
$8(y + 2) = 10y + x$
$8y + 16 = 10y + x$

Step 2: Solve for $x$.
$x = 8y + 16 - 10y$
$x = 16 - 2y$

Step 3: Substitute $x = 16 - 2y$ into the first equation.
$(16 - 2y) + y = 11$
$16 - y = 11$

Step 4: Solve for $y$.
$-y = 11 - 16$
$-y = -5$
$y = 5$

Step 5: Substitute $y = 5$ into $x = 16 - 2y$.
$x = 16 - 2(5)$
$x = 16 - 10 = 6$

$x = 6$, $y = 5$
x = 6,\ y = 5