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To solve the system of equations and find which of the ordered pairs are solutions, we have the following equations:

\[
4x + y = 18
\]
\[
x - 3y = -2
\]

We'll substitute each of the given pairs into both equations to verify if they satisfy both.

### Checking the ordered pairs:
1. **(3, 3)**:
   - Substitute \( x = 3 \) and \( y = 3 \):
     \[
     4(3) + 3 = 12 + 3 = 15 \quad (\neq 18) \rightarrow \text{Not a solution}
     \]
     
2. **(-4, -2)**:
   - Substitute \( x = -4 \) and \( y = -2 \):
     \[
     4(-4) + (-2) = -16 - 2 = -18 \quad (\neq 18) \rightarrow \text{Not a solution}
     \]
     
3. **(5, 1)**:
   - Substitute \( x = 5 \) and \( y = 1 \):
     \[
     4(5) + 1 = 20 + 1 = 21 \quad (\neq 18) \rightarrow \text{Not a solution}
     \]
     
4. **(4, -2)**:
   - Substitute \( x = 4 \) and \( y = -2 \):
     \[
     4(4) + (-2) = 16 - 2 = 14 \quad (\neq 18) \rightarrow \text{Not a solution}
     \]
     
5. **(-4, 2)**:
   - Substitute \( x = -4 \) and \( y = 2 \):
     \[
     4(-4) + 2 = -16 + 2 = -14 \quad (\neq 18) \rightarrow \text{Not a solution}
     \]
     
6. **(4, 2)**:
   - Substitute \( x = 4 \) and \( y = 2 \):
     \[
     4(4) + 2 = 16 + 2 = 18 \quad (\text{Satisfies the first equation})
     \]
     Now check the second equation:
     \[
     4 - 3(2) = 4 - 6 = -2 \quad (\text{Satisfies the second equation})
     \]
   - This pair **is a solution**.

### Conclusion:
The only ordered pair that satisfies both equations is **(4, 2)**.

**Correct answer:** The option **(4, 2)**.

Would you like further details or have any questions? Here are some related questions to expand on this concept:

1. How do you solve a system of equations using the substitution method?
2. What is the elimination method for solving a system of linear equations?
3. How can you determine if a system of equations has no solution, one solution, or infinitely many solutions?
4. What are the graphical interpretations of the solutions to a system of linear equations?
5. How does solving a system of equations differ when the coefficients involve fractions?

**Tip:** When solving a system of equations, always verify the solution by substituting the values back into both equations to confirm consistency.

Select all of the ordered pairs that are solutions to the system: 4x + y = 18 and x - 3y = -2.

Identify the solutions to the system of equations 4x + y = 18 and x - 3y = -2 by checking ordered pairs through substitution. Learn how to solve systems of equations using key algebraic methods. This problem is suitable for students in Grades 9-10.

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