There can be a single solution, an infinite number of solutions, or no solution to a system of two linear equations.
A system is said to be consistent if it has a minimum of one solution. It is independent if a consistent system has only one solution.
Inconsistent equations of linear equations are equations that have no solutions in common. In this system, the lines will be parallel if the equations are graphed on a coordinate plane.
Difference Between Consistent and Inconsistent Systems
A linear or nonlinear system of equations is considered to be consistent in mathematics and especially algebra if at least one set of values for the unknowns satisfies each equation in the system—that is, when substituted into every equation, they make each equation turn true as an identity. The term inconsistent is utilized to delineate a linear or nonlinear equation system in which no set of values for the unknown fulfills all of the equations.
Case 1 : If there are n unknowns in the system of equations and ρ(A) = ρ([A|B]) = n then the system AX = B, is consistent and has a unique solution.
Case 2 : If there are n unknowns in the system AX = B ρ(A) = ρ([A| B]) < N .Then the system is consistent and has infinitely many solutions and these solutions.
Case 3 : If ρ(A) ≠ ρ([A| B]) then the system AX = B is inconsistent and has no solution.
Now, Let's jump in to have fun with, Practically trying them...