That is, any solution of one equation must also be a solution of the other, so the equations depend on each other.
![how to determine which lines overlap origin graphing how to determine which lines overlap origin graphing](https://www.graphpad.com/guides/prism/latest/user-guide/images/appxy1_zoom50.png)
O If the lines are the same (the graphs intersect at all points), the system is a consistent system of linear equations and the equations are dependent. O When a system has no solution (the graphs of the equations don’t intersect at all), the system is an inconsistent system of linear equations and the equations are independent. O When a system has one solution (the graphs of the equations intersect once), the system is a consistent system of linear equationsand the equations are independent. The following terms refer to how many solutions the system has. Some special terms are sometimes used to describe these kinds of systems. When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions. So the coordinates of that point are the solution for the two variables used in the equations. When the lines intersect, the point of intersection is the only point that the two graphs have in common. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations intersect, then there is one solution that is true for both equations.
![how to determine which lines overlap origin graphing how to determine which lines overlap origin graphing](https://assets.rbl.ms/25591222/origin.jpg)
Each shows two lines that make up a system of equations.
![how to determine which lines overlap origin graphing how to determine which lines overlap origin graphing](https://chartio.com/assets/161747/tutorials/charts/area-charts/ade353b657711fcc4a3163aef7116ff61c918921bc29f99fbe3d0177f2f08b15/area-chart-example-2.png)
The graphs of equations within a system can tell you how many solutions exist for that system. The solution for a system of equations is the value or values that are true for all equations in the system.