Final answer:
Two consistent linear systems do not necessarily create another consistent system when combined; consistency depends on the ability to satisfy all equations in the system together. Dimensional consistency in physics ensures equations use compatible units.
Step-by-step explanation:
No, the fact that two linear systems are consistent does not guarantee that another system that combines these will necessarily be consistent. Consistency of a system of linear equations depends on whether there are values for the variables that can simultaneously satisfy all equations in the system. When combining systems, if the combined system has the same number of variables but different equations, it may not be consistent. In order for the combined system to be consistent, it must be able to satisfy all the equations simultaneously without contradiction. This depends on the specific coefficients and constants in the equations, not just the number of variables and equations.
For instance, having a system with equations 7y = 6x + 8, 4y = 8, and y + 7 = 3x shows that we have three different equations with two variables (x and y), and we can determine consistency by trying to solve these equations together. If they share a solution, the system is consistent. In physics, the concept of dimensional consistency is also important because it ensures that equations are using compatible units and measurements, which is essential for physical laws to be valid.