Solution:
Given:
When solving a system of two linear equations, there are three possible cases.
Case 1:
One solution: If the lines intersect, we identify the point of intersection. This is the solution to the system.
The solutions of a system of equations are the values of the variables that make all the equations true.
The solution is represented by (x,y).
The system of equations is consistent independent when it has one solution.
It can be shown graphically below;
Case 2:
No solution: If the lines are parallel, the system has no solution because parallel lines have no common point.
The system of equations is inconsistent when it has no solution.
It can be represented graphically as shown below;
Case 3:
Infinitely many solutions: If the lines are the same, the system has an infinite number of solutions.
The system of equations is consistent dependent when it has an infinite number of solutions.
It can be represented graphically as shown below;