Systems of linear equations when is no solution

The graphs of the lines do not intersect, so the graphs are parallel and there is no solution. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts. The first graph above, "Case 1", 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. Independent system: one solution point. The second graph above, "Case 2", shows two distinct lines that are parallel. Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution.

This is called an "inconsistent" system of equations, and it has no solution. Independent system: one solution and one intersection point. Inconsistent system: no solution and no intersection point. The third graph above, "Case 3", appears to show only one line. Actually, it's the same line drawn twice. These "two" lines, really being the same line, "intersect" at every point along their length.

This is called a "dependent" system, and the "solution" is the whole line. Number of solutions to a system of equations algebraically. Practice: Number of solutions to a system of equations algebraically.

How many solutions does a system of linear equations have if there are at least two? Number of solutions to system of equations review. Next lesson. If you plot the two lines corresponding to the two equations you will see that they are parallel! How does a system of linear equations have no solution?

May 7, I tried this:.