To find the values of \( x \) and \( y \) in the equation \( 7x - 5y = 24 \), we need more information, such as a second equation involving \( x \) and \( y \). With just one equation, we can only express one variable in terms of the other. Here’s how we can solve for one variable in terms of the other:

### Step 1: Solve for \( x \) in terms of \( y \)
Start with the given equation:
\[
7x - 5y = 24
\]
Solve for \( x \):
\[
7x = 24 + 5y
\]
\[
x = \frac{24 + 5y}{7}
\]

### Step 2: Solve for \( y \) in terms of \( x \)
Alternatively, solve for \( y \) in terms of \( x \):
\[
7x - 5y = 24
\]
\[
-5y = 24 - 7x
\]
\[
y = \frac{7x - 24}{5}
\]

Since we don't have a second equation, this is the best we can do: express each variable in terms of the other. If you provide another equation or some additional condition, I can help solve for the exact values of \( x \) and \( y \).

Would you like further details or clarification? Here are some related questions that might interest you:

1. How do we solve systems of linear equations?
2. What are methods for solving two-variable linear equations, like substitution and elimination?
3. How does graphing help visualize solutions to two-variable equations?
4. What are dependent and independent variables in a system of equations?
5. How can we apply systems of equations in real-world problems?

**Tip:** If you're given only one equation with two variables, always look for additional information or constraints to find unique solutions.

Learn how to solve the linear equation 7x - 5y = 24 by expressing x in terms of y or y in terms of x. This problem covers key algebraic concepts in two-variable systems and is suitable for students in Grades 8-10.

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