How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #6x-7y=28# & #6x-3y=12#?
Graph, and find the solution(s), if any.
This system is consistent and independent.
One solution = Consistent, independent
No solution = Inconsistent
Infinite solutions = Consistent, dependent
Graphing the two equations gives this graph:
As you can see, the two lines intersect at the point
Because of this, there is only one solution to the system of equations:
This system is consistent; a consistent system of linear equations has at least one solution (at least one intersection point), and an inconsistent system of linear equations has no solution (no intersection points).
This system is also independent; an independent system has only one solution (one intersection point), while a dependent system has an infinite amount of solutions (the lines match up perfectly; an infinite amount of intersection points).