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:

solution to the system
the two equations
the result if the system was solved algebraically

Answer 1

If the lines overlap, then the equations are scalar multiples of the other.

For instance:

The lines x+y = 1 and 2x+2y = 2 would overlap as indicated.

This tells you that if you should solve the system algebraically that you would get a true statement like 1=1 and this would indicate that the system had infinitely many solutions provided that both the x and y coordinate lie on that line.

Answer 2

Okay..