If `(x-2,y+5)=(2,(1)/(3))` are two equal ordered pairs, then `x=4, y=(-14)/(3)`

Explanation

To solve the problem, we need to determine the values of \( x \) and \( y \) from the given ordered pairs. The ordered pairs are given as \( (x-2, y+5) = (2, \frac{1}{3}) \).

### Step-by-Step Solution:

1. **Set up the equations from the ordered pairs**:
Since the ordered pairs are equal, we can equate the corresponding components:
\[ x - 2 = 2 \quad \text{(1)} \]
\[ y + 5 = \frac{1}{3} \quad \text{(2)} \]

2. **Solve for \( x \)**:
From equation (1):
\[ x - 2 = 2 \]
To isolate \( x \), add 2 to both sides:
\[ x = 2 + 2 \]
\[ x = 4 \]

3. **Solve for \( y \)**:
From equation (2):
\[ y + 5 = \frac{1}{3} \]
To isolate \( y \), subtract 5 from both sides:
\[ y = \frac{1}{3} - 5 \]
To perform the subtraction, convert 5 into a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
Now, subtract:
\[ y = \frac{1}{3} - \frac{15}{3} = \frac{1 - 15}{3} = \frac{-14}{3} \]

4. **Conclusion**:
We have found the values:
\[ x = 4 \quad \text{and} \quad y = -\frac{14}{3} \]

### Final Answer:
Thus, the statement that \( x = 4 \) and \( y = -\frac{14}{3} \) is true.

---