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To solve the given system by substitution, let's analyze the two equations:

1. \( 5x + 4y = 33 \)
2. \( x = 4y - 3 \)

### Step-by-Step Solution

1. **Substitute** the expression for \( x \) from the second equation into the first equation:
   \[
   5(4y - 3) + 4y = 33
   \]

2. **Expand and simplify**:
   \[
   20y - 15 + 4y = 33
   \]
   \[
   24y - 15 = 33
   \]

3. **Solve for \( y \)**:
   \[
   24y = 48
   \]
   \[
   y = 2
   \]

4. **Substitute \( y = 2 \) back into the second equation** to find \( x \):
   \[
   x = 4(2) - 3
   \]
   \[
   x = 8 - 3 = 5
   \]

### Solution
The solution is \( (x, y) = (5, 2) \).

### Answer Choice
This corresponds to **Option A: The solution is (5, 2)**.

Would you like further details, or do you have any questions?

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### Related Questions to Explore
1. How does the substitution method work for systems of equations?
2. Can the substitution method be used for non-linear systems?
3. What is the elimination method, and when is it preferred over substitution?
4. How can graphing be used to solve systems of equations?
5. What are some practical applications of solving systems of equations?

### Tip
When solving systems by substitution, always isolate one variable in the simplest equation to reduce the complexity of your work.

Solve the system of equations by the substitution method:
5x + 4y = 33
x = 4y - 3

Discover how to solve the system of equations 5x + 4y = 33 and x = 4y - 3 using the substitution method. This step-by-step guide demonstrates substitution and solving techniques, ideal for students in Grades 8-10.

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