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Since the lines that intersect are the equations, if they intersect once they have one solution.
If a system is inconsistent it cannot have any solutions.A system of equations is considered inconsistent when the lines are parallel which means they never intersect so there are no solutions.A system is considered consistent when they intersect at one point and have one solution (Also known as an independent system of equations).Dependent Systems are when the lines coincide (the same equation) so they have an infinite number of solutions.
A consistent system of equations is one in which there is at least one set of values for the variables that satisfies all the equations simultaneously. In graphical terms, this means that the lines or planes represented by the equations intersect at one or more points. A consistent system can be classified as either independent (with a unique solution) or dependent (with infinitely many solutions). In contrast, an inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.