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How many solutions can two lines have that intersect once?
Since the lines that intersect are the equations, if they intersect once they have one solution.
How many solutions does an inconsistent system of equations have?
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.
Why do people call it a system when two lines 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.
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
How do you know which region of the graph of a system of linear inequalities contains the solutions?
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
