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Coincident Lines
Coincident lines are two lines in a coordinate plane that lie exactly on top of each other — they are the same line. This occurs when both lines share the same slope and the same -intercept. Because every point on one line is also a point on the other, the two linear equations have identical graphs. When a system of two linear equations produces coincident lines, every ordered pair on the shared line satisfies both equations simultaneously, so the system has infinitely many solutions.
Coincident lines can be recognized by converting both equations to slope-intercept form : if both equations yield the same values of and , the lines are coincident. This distinguishes them from parallel lines, which share the same slope but have different -intercepts and therefore never intersect.
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