We need to solve the following system of equations using the substitution method: $\frac{1}{2}x - \frac{1}{8}y = 4$ (1) $\frac{3}{4}x + \frac{2}{5}y = 6$ (2)

1. Problem Description

We need to solve the following system of equations using the substitution method:

$\frac{1}{2}x - \frac{1}{8}y = 4$ (1)

$\frac{3}{4}x + \frac{2}{5}y = 6$ (2)

2. Solution Steps

First, we can multiply both equations by constants to eliminate the fractions.

Multiply the first equation by 8:

$8(\frac{1}{2}x - \frac{1}{8}y) = 8(4)$

$4x - y = 32$ (3)

Multiply the second equation by 20:

$20(\frac{3}{4}x + \frac{2}{5}y) = 20(6)$

$15x + 8y = 120$ (4)

Now we can isolate y in equation (3):

$y = 4x - 32$ (5)

Substitute equation (5) into equation (4):

$15x + 8(4x - 32) = 120$

$15x + 32x - 256 = 120$

$47x = 376$

$x = \frac{376}{47}$

$x = 8$

Now substitute the value of x back into equation (5) to find y:

$y = 4(8) - 32$

$y = 32 - 32$

$y = 0$

Therefore, the solution to the system of equations is $x = 8$ and $y = 0$.

3. Final Answer

(8, 0)