what is the condition of of intersecting line in a a pair of linear equation in a two variables
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A necessary condition for two lines to intersect is that they are in the same plane—that is, are not skew lines. Satisfaction of this condition is equivalent to the tetrahedron with vertices at two of the points on one line and two of the points on the other line being degenerate in the sense of having zero volume.
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If two lines are intersecting then, they have unique solution and pair of linear equations is consistent. If we draw a rough graph of both the lines (as shown below) we will find that both lines are parallel. So, they have no solution
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