The problem is to solve for $x$ and $y$ in the equation $\frac{1}{2}x + \frac{3}{4}y = 5$. However, since we only have one equation and two variables, we can only express one variable in terms of the other.

1. Problem Description

The problem is to solve for $x$ and $y$ in the equation $\frac{1}{2}x + \frac{3}{4}y = 5$. However, since we only have one equation and two variables, we can only express one variable in terms of the other.

2. Solution Steps

We want to isolate $x$ or $y$. Let's isolate $x$.

We have $\frac{1}{2}x + \frac{3}{4}y = 5$.

Subtract $\frac{3}{4}y$ from both sides:

$\frac{1}{2}x = 5 - \frac{3}{4}y$

Multiply both sides by 2:

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

$x = 10 - \frac{6}{4}y$

$x = 10 - \frac{3}{2}y$

Alternatively, let's isolate $y$.

We have $\frac{1}{2}x + \frac{3}{4}y = 5$.

Subtract $\frac{1}{2}x$ from both sides:

$\frac{3}{4}y = 5 - \frac{1}{2}x$

Multiply both sides by $\frac{4}{3}$:

$y = \frac{4}{3}(5 - \frac{1}{2}x)$

$y = \frac{20}{3} - \frac{4}{6}x$

$y = \frac{20}{3} - \frac{2}{3}x$

3. Final Answer

Since there is only one equation, we can only express $x$ in terms of $y$, or $y$ in terms of $x$.

$x = 10 - \frac{3}{2}y$

or

$y = \frac{20}{3} - \frac{2}{3}x$