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!
If the system has no solution, then it is said to be inconsistent system.
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. Graphing Systems of Linear Equations. You may have heard of independent variables, but did you know that systems of equations can be independent ? The first graph above, Case shows two distinct non-parallel lines that cross at exactly one point. This is called an independent system of equations , and the solution is always some x,y-point. An example is: State whether each system is consistent and dependent, .