Solve the equation `(1)/(3)y+5=8` by the trial-and-error method.

Answer

To solve the equation \(\frac{1}{3}y + 5 = 8\) using the trial-and-error method, we will substitute different values for \(y\) until the left-hand side equals the right-hand side.

### Step-by-Step Solution:

1. **Start with the equation**:
\[ \frac{1}{3}y + 5 = 8 \]

2. **Choose a value for \(y\)**:
Let's start with \(y = 3\).
\[ \frac{1}{3}(3) + 5 = 1 + 5 = 6 \]
The left-hand side equals 6, which does not equal 8.

3. **Try the next value for \(y\)**:
Now, let's try \(y = 6\).
\[ \frac{1}{3}(6) + 5 = 2 + 5 = 7 \]
The left-hand side equals 7, which still does not equal 8.

4. **Try another value for \(y\)**:
Next, let's try \(y = 9\).
\[ \frac{1}{3}(9) + 5 = 3 + 5 = 8 \]
The left-hand side equals 8, which matches the right-hand side.

5. **Conclusion**:
We found that when \(y = 9\), both sides of the equation are equal. Therefore, the solution to the equation \(\frac{1}{3}y + 5 = 8\) is:
\[ y = 9 \]