Answer: D. $3$

Explanation:1. Understand the condition for infinitely many solutions: A system of two linear equations has infinitely many solutions if and only if the two equations represent the same line. This means their slopes must be equal, and their y-intercepts must be equal.

2. Identify the slope and y-intercept of the first equation: The first equation is $y = 27x + 3$. This is in the slope-intercept form $y = (\text{slope})x + (\text{y-intercept})$. So, for the first equation: Slope = $27$ y-intercept = $3$

3. Identify the slope and y-intercept of the second equation: The second equation is given as $y = mx + b$. Slope = $m$ y-intercept = $b$

4. Apply the condition for infinitely many solutions: For the two lines to be identical: The slopes must be equal: $m = 27$. The y-intercepts must be equal: $b = 3$.

5. Determine the value of b: From the above, the value of b must be $3$.

Conclusion:If the system has infinitely many solutions, the value of b must be $3$.