Explanation:

To have an infinite number of solutions, two equations must be proportional. So, we need to make the equation:

$$\frac{17}{23}=\frac{m}{299}=\frac{102}{138}$$

- Simplify $\frac{102}{138}$. It reduces to $\frac{17}{23}$.

- Thus, $\frac{102}{138}=\frac{17}{23}$. This confirms proportionality with the first equation.

- Now equate $\frac{m}{299}$ to $\frac{17}{23}$.

- Solve for $m$ in the equation:

$$

\frac{m}{299} = \frac{17}{23}

$$

- Cross-multiply to find $m$:

$$

m = \frac{17 \times 299}{23}

$$

- Calculate:

$$

m = 221

$$

- Thus, Option 1: 221 is the correct answer.

Option:1, 221 is correct.