Find the solution of the following equations by trial-and-error method.
`(1)/(3)y+5=8`

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 we find the one that satisfies the equation.

### Step-by-Step Solution:

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

2. **Choose a value for \(y\)**:
Let's start with \(y = 1\).

3. **Substitute \(y = 1\) into the equation**:
\[ \frac{1}{3}(1) + 5 = \frac{1}{3} + 5 \]
To combine the terms, we can convert 5 into a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
So,
\[ \frac{1}{3} + \frac{15}{3} = \frac{16}{3} \]
This is not equal to 8.

4. **Choose a new value for \(y\)**:
Next, let's try \(y = 3\).

5. **Substitute \(y = 3\) into the equation**:
\[ \frac{1}{3}(3) + 5 = 1 + 5 = 6 \]
This is not equal to 8.

6. **Choose another value for \(y\)**:
Now, let's try \(y = 6\).

7. **Substitute \(y = 6\) into the equation**:
\[ \frac{1}{3}(6) + 5 = 2 + 5 = 7 \]
This is also not equal to 8.

8. **Choose another value for \(y\)**:
Let's try \(y = 9\).

9. **Substitute \(y = 9\) into the equation**:
\[ \frac{1}{3}(9) + 5 = 3 + 5 = 8 \]
This is equal to 8.

10. **Conclusion**:
Since substituting \(y = 9\) gives us the left-hand side equal to the right-hand side, we have found the solution. Therefore, the required value of \(y\) is:
\[ y = 9 \]