Final answer:
Consistent linear systems Ax = b1 and Ax = b2 mean that there exists at least one solution x for each equation. A being consistent across both implies it's the same matrix in each equation, which can then be analyzed or solved using appropriate linear algebra techniques.
Step-by-step explanation:
When we say that the linear systems Ax = b1 and Ax= b2 are both consistent, it means there exists at least one solution x for each system. That is, there are values of the variable x that satisfy the equation Ax = b1 and also values of x that satisfy Ax = b2, where A is a matrix and b1 and b2 are vectors.
If the constant A is the same for two equations, you could, under certain circumstances, isolate In A (presuming In A refers to the natural logarithm of A) and set the resulting expressions equal to one another if they equate to the same function of A. But in the context of linear systems, we are more focused on solving for the vector x rather than manipulating constants or logarithms.