The complex numbers $z$ and $w$ satisfy the following equations. $4z + 5iw = 7$
$(1 - i)z + 8w = 30$ Find $z$ and $w$, giving your answers in the form $a + ib$ where $a$ and $b$ are real numbers.

1. Multiply the equations by suitable factors to align the coefficients of $z$.

Multiply the first equation by $(1 - i)$ and the second by $4$:
$4(1 - i)z + 5i(1 - i)w = 7(1 - i)$
$4(1 - i)z + 32w = 120$

2. Subtract the equations to eliminate $z$ and simplify the $w$ terms.

Subtract the first equation from the second:
$32w - 5i(1 - i)w = 120 - 7(1 - i)$
$(32 - 5i + 5i^2)w = 120 - 7 + 7i$
$(32 - 5i - 5)w = 113 + 7i$
$(27 - 5i)w = 113 + 7i$

3. Solve for $w$ by multiplying the numerator and denominator by the complex conjugate.

$w = \frac{113 + 7i}{27 - 5i}$
$w = \frac{(113 + 7i)(27 + 5i)}{(27 - 5i)(27 + 5i)}$
$w = \frac{3051 + 565i + 189i + 35i^2}{27^2 + 5^2}$
$w = \frac{3051 - 35 + 754i}{729 + 25}$
$w = \frac{3016 + 754i}{754}$
$w = 4 + i$

4. Substitute $w$ back into the first equation to find $z$.

$4z + 5i(4 + i) = 7$
$4z + 20i + 5i^2 = 7$
$4z + 20i - 5 = 7$
$4z = 12 - 20i$
$z = 3 - 5i$