The ordered pair (0, 4) is a solution of which system?

To determine which system of equations has the ordered pair \((0, 4)\) as a solution, we need to check where \(x = 0\) and \(y = 4\) satisfy both equations in the system. 

Here are the steps you can follow to identify the system:

1. **Substitute \(x = 0\) and \(y = 4\) into the first equation of the system.**
2. **Substitute \(x = 0\) and \(y = 4\) into the second equation of the system.**
3. **Verify that both equations are true with these values.**

If both equations are satisfied, then \((0, 4)\) is a solution to that system.

### Example of Systems to Test

Let's test \((0, 4)\) against some hypothetical systems:

1. **System A:**
   \[
   \begin{cases}
   y = 4x + 4 \\
   y = 2x + 4
   \end{cases}
   \]

   - Substitute \((0, 4)\):
     - \(4 = 4(0) + 4 \Rightarrow 4 = 4\) (True)
     - \(4 = 2(0) + 4 \Rightarrow 4 = 4\) (True)

   Since both equations are satisfied, \((0, 4)\) is a solution to System A.

2. **System B:**
   \[
   \begin{cases}
   y = 3x + 1 \\
   y = -2x + 4
   \end{cases}
   \]

   - Substitute \((0, 4)\):
     - \(4 = 3(0) + 1 \Rightarrow 4 = 1\) (False)
     - \(4 = -2(0) + 4 \Rightarrow 4 = 4\) (True)

   Only one equation is satisfied. Thus, \((0, 4)\) is **not** a solution to System B.

3. **System C:**
   \[
   \begin{cases}
   y = 4 \\
   x = 0
   \end{cases}
   \]

   - Substitute \((0, 4)\):
     - \(4 = 4\) (True)
     - \(0 = 0\) (True)

   Both equations are satisfied. So, \((0, 4)\) is a solution to System C.

### Conclusion

Based on the hypothetical examples above, \((0, 4)\) is a solution to both System A and System C but not System B. You would need to identify or be given specific systems of equations to test \((0, 4)\) as a solution to see which applies.

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How can we determine if an ordered pair is a solution to a system of linear equations in three variables?
2. What are the possible types of solutions a system of linear equations can have?
3. How can we graphically interpret the solution of a system of equations?
4. How does substitution work to solve a system of equations?
5. What is the difference between consistent and inconsistent systems of equations?

**Tip:** When verifying solutions to a system of equations, always substitute the given values into each equation to ensure they satisfy both equations simultaneously.

Learn how to identify systems of linear equations where the ordered pair (0, 4) is a solution. Understand the process of substitution and verification to determine if specific systems satisfy the given solution. Suitable for students and learners studying systems of equations in mathematics.

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