If the system has at least one solution (one solution or infinitely many solutions), it is said to be consistent system. When you graph the equations, both equations represent the same line. The graphs of the lines do not intersect, so the graphs . That means that those equations intersect only at that one point. That kind of solution is called consistent and independent !
This tutorial explains systems with one solution and even shows you an example!
You may have heard of independent variables, but did you know that systems of equations can be independent?
The following figure will give clear picture of what we have learnt above. Examples: Discuss the number of solutions and type of the system of equations given in the graphs. All examples shown are linear systems. A consistent independent system of equations will have one solution. Inconsistent systeno solution and no intersection point.
Independent systeone solution and one intersection point. The equations can be viewed algebraically or graphically.