State whether the following set of equations is independent-consistent, dependent-consistent, dependent-inconsistent or independent-inconsistent: y = 3 3x = 8 - 3y
A set of equations is consistent if there is a solution for the system of equations. A set of equations is independent if there is only one solution for it and dependent if there are an infinite number of solutions.
The set of equations we have is y = 3 and 3x = 8 - 3y
Solving the two we have y = 3 and x = -1/3
There is only one solution (-1/3, 3).
The set of equations is therefore consistent and independent.