If (x,y) is a solution to the system of equations above, what is the value of `x ^(2)` ?

Explanation

To solve the problem step by step, we need to analyze the given system of equations.

### Step 1: Identify the equations
We have the following equations:
1. \( y = 2x \)
2. \( 2x^2 + 2y^2 = 240 \)

### Step 2: Substitute \( y \) in the second equation
Since we know that \( y = 2x \), we can substitute \( y \) in the second equation:
\[ 2x^2 + 2(2x)^2 = 240 \]

### Step 3: Simplify the equation
Now, we simplify the equation:
\[ 2x^2 + 2(4x^2) = 240 \]
This simplifies to:
\[ 2x^2 + 8x^2 = 240 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 10x^2 = 240 \]

### Step 5: Solve for \( x^2 \)
To find \( x^2 \), divide both sides by 10:
\[ x^2 = \frac{240}{10} \]
\[ x^2 = 24 \]

### Final Answer
Thus, the value of \( x^2 \) is \( 24 \).

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