Question

Consider the system:

y = 3x + 5
y = ax + b
What values for a and b make the system
inconsistent? What values for a and b make the
system consistent and dependent? Explain

Answer 1

An exponent value in a would make the system inconsistent because it will either gain or lose height over time.

Any real number without an exponent value will make the system consitent.

Any infintite/repeating number will make the system both consistent and inconsistent. it is consisent because it will stay at a constant rate but also inconsistent because it is repeating and will never end.

Answer 2

When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.