The given graphs of the system of equations will have an infinite solution, unique solution and no solution, respectively.
What is a system of equations?
The types of system of equations in mentioned below.
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
A.) For the first graph since the lines overlap or lie on each other, therefore, the given system of equation in the first graph will be of Dependent consistent system. Thus, the system will have an infinite number of solutions.
B.) For the second graph since the lines intersect at a particular point, therefore, the given system of equations in the second graph will be an Independent consistent system. Thus, the system will have a unique solution number of solutions. Also, the solution of the equation is the point at which the lines intersect, therefore, the solution of the system of the equation will lie at (-1,2.)
C.) For the third graph since the lines are parallel to each other, therefore, the given system of equations in the third graph will be an Independent consistent system. Thus, the system will have no solutions.
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