https://file.aiquickdraw.com/mathbot/file/1727385448675plohbq2y.jpg

Let's analyze the given system of equations:

\[
4x + 4y = 52 \quad \text{(Equation 1)}
\]
\[
2x + y = 16 \quad \text{(Equation 2)}
\]

We are tasked with finding which system from the options has the same solution as this system.

### Step 1: Simplify the given system

To make the system easier to compare, let's simplify the second equation by multiplying it by 2:

\[
2(2x + y) = 2(16) \quad \Rightarrow \quad 4x + 2y = 32
\]

So, the system becomes:
\[
4x + 4y = 52 \quad \text{(Equation 1, unchanged)}
\]
\[
4x + 2y = 32 \quad \text{(Simplified Equation 2)}
\]

### Step 2: Analyze the options

We now look for a system that matches or is equivalent to this simplified system.

#### Option A: 
\[
4x + 4y = 52 \quad \text{and} \quad -4x + y = -32
\]
This system does not match the original system.

#### Option B: 
\[
4x + 4y = 52 \quad \text{and} \quad -4x - 2y = -32
\]
This system also does not match the original system.

#### Option C: 
\[
4x + 4y = 52 \quad \text{and} \quad -4x + y = -32
\]
This is the same as option A, which we already saw does not match.

#### Option D: 
\[
4x + 4y = 52 \quad \text{and} \quad 2x - 2y = 16
\]
This option also does not match the original system.

None of these options exactly matches the simplified system, but it's possible some options correspond to the system under transformations (such as multiplying equations by constants).

Which system of equations has the same solution as the system below? 4x + 4y = 52 and 2x + y = 16.

Determine which system of equations has the same solution as the system 4x + 4y = 52 and 2x + y = 16. Learn how to simplify and compare systems of equations using algebraic techniques. Suitable for Grades 8-10.

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