Final answer:
The statement is b) false; two equivalent linear systems have the exact same solution set, because being equivalent means that all solutions that satisfy one system also satisfy another.
Step-by-step explanation:
The statement that two equivalent linear systems can have different solution sets is false. When we say that two linear systems are equivalent, it means that they have the same solution set.
Even though the equations in the systems may appear different, if they are indeed equivalent, they will have the same set of values that satisfy all equations in both systems.
For instance, consider the linear system with equations y = 2x + 3 and 2y = 4x + 6. Although they look different, the second equation is simply the first equation multiplied by 2, hence they are equivalent and share the same solution set.
As per the examples provided, results of simulations, physical displacements, the Pythagorean theorem, wave interactions, and vector components are all relevant within their respective contexts, but they reinforce the concept that equivalency in mathematical terms dictates identical outcomes or solutions.