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Which system of equations has the same solution as the system below?

The problem is asking us to identify which alternative system of equations has the same solution as the given system:

\[
\begin{cases} 
5x + 4y = 36 \\
2x + 2y = 14 
\end{cases}
\]

To find the correct answer, we need to check each option to see if the system is equivalent to the original one. Here’s how we can analyze this:

1. **Simplify the second equation in the original system**: 
   \[
   2x + 2y = 14
   \]
   Dividing by 2:
   \[
   x + y = 7
   \]
   
   This equation, \(x + y = 7\), is another form of the second equation in the system. The solutions for \(x\) and \(y\) in the new forms will remain consistent with the original.

2. **Check each answer option** to see if it matches the equivalent form of the original system.

Let’s go through each choice and determine whether they lead to the same solution.

Would you like a full solution for each option, or a specific answer only?

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If you want further details or more practice, here are some follow-up questions:

1. How can we identify equivalent systems of equations quickly?
2. What techniques are useful to simplify systems of equations?
3. What are common mistakes to avoid when working with equivalent equations?
4. How do elimination and substitution help solve systems of equations?
5. Why do multiplying or dividing equations by a constant not change the solution?

**Tip:** When working with systems of equations, always simplify them to their simplest form to see equivalent solutions more clearly.

Which system of equations has the same solution as the system below?

5x + 4y = 36
2x + 2y = 14

Learn how to identify an equivalent system of linear equations for the given equations 5x + 4y = 36 and 2x + 2y = 14. Understand the methods for simplifying equations and determining equivalence for consistent solutions.

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