Question

How many solutions does this system of equations have? y=3x+5 and x+y=5

Answer 1

can you solve the 2nd one for "y"?

Answer 2

I think so

Answer 3

so... what did you get for "y"?

Answer 4

For y I got 5 and X i got 0

Answer 5

hmm how did you get those?

Answer 6

It's the opposite actually.
x = 0
y = 5
if you did mess that up?..

Answer 7

Yeah that What i meant. I looked at my paper wrong

Answer 8

heehh

Answer 9

anyhow, I meant to "solve", that is, "isolate" "y"

once you do so you can tell its slope
then you can compare the slopes of both functions, and that'd say how many solutions it has or not

Answer 10

Well since both x and y have an answer that means there is only one solution.

Answer 11

right

Answer 12

A couple of things to remember:

If two lines in the same plane have different slopes, they will intersect in one point; the two equations have a unique solution.

If two lines in the same plane have the same slope, but different y-intercepts, they'll never intersect; there's no solution.

If two lines in the same plane have the same slope and same y-intercept, they coincide, and there will be infinitely many solutions.