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Question
if a system of linear equations has one solution, what does this mean about the two lines? parallel lines the same line intersecting lines
A system of linear equations represents two lines. If there is one solution, it means there is one point \((x,y)\) that satisfies both equations. Geometrically, this occurs when the two lines cross each other at exactly one point. Parallel lines have no solution (they never meet), and the same line has infinitely many solutions (all points on the line satisfy both equations).
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Intersecting lines