Question

You graph a system of equations and the two lines overlap, or lie right on top of one another. Explain what this tells you about the:1.solution to the system
2.the two equations
3.the result if the system was solved algebraically

Answer 1

if they overlap then there is one solution to the system (x,y)

if they lie on top of one another there are no solutions

Answer 2

Jimmy Rep, if they overlap, that means there are infinite solutions

Answer 3

The solution is the points the two lines have in common. If they have more than one point in common (that is they intersect in a single point) then they have all points in common. So the solution is every point on the line is a solution of both equations since both equations represent the same line. For example, if the system is:

x+y=6
2x+2y = 12
The solution is [(x,y)| x+y=6]