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No Solutions for a System of Linear Equations

Explanation

No Solutions for a System of Linear Equations

If a system has no solution, its graph might look similar to the graph shown.

No solution linear system of equations.svg

Recall that the solution to a system is the point where the lines intersect. If a system has no solution, it must be then that the lines never intersect. In fact, the lines must be parallel, meaning that they have the same slope and different -intercepts. An example of one such system is