The solution set of `xge5, yge0` and `xle5,yle0` is

Options

A. `xge-5,y=0`
B. `x=5,y=0`
C. `xge-5,yle0`
D. `xle-5,yle0`

Answer

To solve the given inequalities \( x \geq 5, y \geq 0 \) and \( x \leq 5, y \leq 0 \), we will analyze each inequality step by step.

### Step 1: Analyze the inequalities for \( x \)

1. The first inequality is \( x \geq 5 \).
- This means that \( x \) can take any value starting from 5 and going towards positive infinity.
- On a number line, we would represent this as a closed circle at 5 and shading to the right.

2. The second inequality is \( x \leq 5 \).
- This means that \( x \) can take any value starting from negative infinity up to 5.
- On a number line, we would represent this as a closed circle at 5 and shading to the left.

### Step 2: Find the intersection for \( x \)

- The intersection of \( x \geq 5 \) and \( x \leq 5 \) is where both conditions are satisfied.
- The only value that satisfies both inequalities is \( x = 5 \).

### Step 3: Analyze the inequalities for \( y \)

1. The first inequality is \( y \geq 0 \).
- This means that \( y \) can take any value starting from 0 and going towards positive infinity.
- On a number line, we would represent this as a closed circle at 0 and shading upwards.

2. The second inequality is \( y \leq 0 \).
- This means that \( y \) can take any value starting from negative infinity up to 0.
- On a number line, we would represent this as a closed circle at 0 and shading downwards.

### Step 4: Find the intersection for \( y \)

- The intersection of \( y \geq 0 \) and \( y \leq 0 \) is where both conditions are satisfied.
- The only value that satisfies both inequalities is \( y = 0 \).

### Final Solution

Thus, the solution set for the given inequalities is:
\[ (x, y) = (5, 0) \]