infinitely many 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.
no solutions
One solution
parallel
If you graph a system of two lines and all you see is one line, this means that both lines are the same. Any point on the line is a solution, so the system has an infinite number of solutions.
No Solutions
Correct. Unless the parallel lines are coincident, in which case the solution set is the whole line.
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.
no solutions
If you graph the two functions defined by the two equations of the system, and their graphs are two parallel line, then the system has no solution (there is not a point of intersection).
one solution
One solution
The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
parallel
Although there is no graph, the number of solutions is 0.
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.