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

@Compassionate

Answer 1

There's no solution if the lines overlap, right? Or is that just my tired brain talking.

Answer 2

@jim_thompson5910

Answer 3

you must be tired because two lines that overlap will intersect an infinite amount of times

Answer 4

so there are infinitely many solutions (all on the lines that overlap)

this system is then known to be a dependent system (since one equation depends on the other)

Answer 5

Oh jeez. Way off. What about #2?

Answer 6

well the two equations would be very similar since one equation would just be a scalar multiple of the other

Answer 7

ex: x+y = 10 and 2x+2y = 20 form a dependent system of equations

Answer 8

since you're doubling everything in x+y=10 to get 2x+2y=20

Answer 9

and the third?

Answer 10

at the very end, you would get 0=0, which is always true

that leads to the fact that there are infinitely many solutions

Answer 11

Thanks :)

Answer 12

yw