Final answer:
The viable solutions to the system of inequalities representing stock prices over time are all real number values with x>=0 and y>=0, as both time and price per share cannot be negative.
Step-by-step explanation:
The system of equations provided models the price per share for two different stocks over time. We have two inequalities to consider:
-y <= 3x + 4
-3x + 3y <= -9
To find the viable solutions to this system, we look for the values of x and y that satisfy both inequalities simultaneously. Since the system represents prices and time, both variables are typically non-negative in such contexts. Thus, the viable solutions should be all real number values of x and y such that x is greater than or equal to 0 (x>=0) since time cannot be negative and y represents the price per share, which also cannot be negative. Therefore, the correct answer is 'All real number values, with x>=0 and y>=0'.