Solving Linear Systems of Equations by Graphing
Procedure —
To Solve a Linear System of Equations By Graphing
Graph each line on the same coordinate axes.
There are three possible outcomes:
| • The lines intersect at exactly one point.
The system has exactly one solution.
The solution is the coordinates of the point of intersection.
The system is consistent.
The equations are independent.
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| • The lines do not intersect.
The system has no solution because the lines have no points
in common.
The system is inconsistent.
The equations are independent.
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| • The lines coincide.
The system has infinitely many solutions.
The solutions may be
stated by writing one of the equations of the system.
The system is consistent.
The equations are dependent. |
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