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

To determine which system of equations has \((0, 4)\) as a solution, we need to substitute \(x = 0\) and \(y = 4\) into each equation of the system. If both equations are satisfied, then \((0, 4)\) is indeed a solution to that system.

Let's consider a general system of two linear equations:

1. \(ax + by = c\)
2. \(dx + ey = f\)

Substitute \(x = 0\) and \(y = 4\) into these equations:

1. \(a(0) + b(4) = c \Rightarrow 4b = c\)
2. \(d(0) + e(4) = f \Rightarrow 4e = f\)

The pair \((0, 4)\) will be a solution for the system if both equations hold true after the substitution. Therefore, the system where \(c = 4b\) and \(f = 4e\) will have \((0, 4)\) as a solution.

If you have specific systems of equations you'd like to evaluate, I can help determine which one has \((0, 4)\) as a solution.

Would you like to explore specific systems of equations? Or would you like more detailed explanations? 

Here are five relative questions to expand on this:

1. How do you solve a system of linear equations using substitution?
2. Can a point be a solution to more than one system of linear equations?
3. What is the geometric interpretation of a solution to a system of equations?
4. How can you determine if a system of equations has no solution?
5. What does it mean for a system of equations to be dependent?

**Tip:** When testing if an ordered pair is a solution to a system of equations, always substitute the values into both equations to ensure they satisfy both.

Discover which system of linear equations contains the ordered pair (0, 4) as a solution. Explore the application of the substitution method to verify the solution. Suitable for Grades 9-12 mathematics education.

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