I. ` sqrt(361x) + sqrt(16) = 0`
II. `sqrt(441) y + 4 = 0`

Options

A. ` x gt y`
B. ` x ge y`
C. `x lt y`
D. `x le y`

Explanation

Let's solve the equations step by step.

### Step 1: Solve the first equation
The first equation is:
\[ \sqrt{361x} + \sqrt{16} = 0 \]
We know that \(\sqrt{16} = 4\). So we can rewrite the equation as:
\[ \sqrt{361x} + 4 = 0 \]

### Step 2: Isolate the square root
Next, we isolate the square root term:
\[ \sqrt{361x} = -4 \]
However, since the square root of a number cannot be negative, this equation has no solution in real numbers. Thus, we conclude:
\[ \text{No real solution for } x. \]

### Step 3: Solve the second equation
Now, let's solve the second equation:
\[ \sqrt{441}y + 4 = 0 \]
We know that \(\sqrt{441} = 21\). So we can rewrite the equation as:
\[ 21y + 4 = 0 \]

### Step 4: Isolate \(y\)
Now, we isolate \(y\):
\[ 21y = -4 \]
Then, divide both sides by 21:
\[ y = -\frac{4}{21} \]

### Step 5: Summarize the solutions
We have found:
- For the first equation, there is no real solution for \(x\).
- For the second equation, the solution for \(y\) is:
\[ y = -\frac{4}{21} \]

### Step 6: Relation between \(x\) and \(y\)
Since there is no valid value for \(x\) (as it leads to a contradiction), we cannot establish a numerical relation between \(x\) and \(y\). However, we can state that \(x\) does not exist in the real number system, while \(y\) is a negative value.