Question

Given the equation 3x +5y =7 Write a new equation state uses
- 1 intersection pint
-infinite
-None

Answer 1

to have one intersection point, you only need the lines to not be parallel. So just change up the slop a little and youre good to go ex: 1x+5y=7 would be skew and therefore have 1 point of intersection

to have infinite, they must be the same line. you could do this any number of ways. the simplest way is to do the same thing to both sides of the equation like multiply by 2 or something and then its technically 2 different equations representing the same line

finally, to have 0 solutions, the lines must be parallel but not the same. you can do this by changing only one side of the original equation but not to the other ex: 3x+7y=2

Answer 2

May want to change terminology on "skew lines", since skew lines lie in parallel planes and so do not intersect. ;)

Answer 3

right you are... haha good catch!

Answer 4

But the last graph is a pair of intersecting lines that lie in the same plane, and so yes that system does have one solution. :)

Answer 5

I can't ever draw nice graphs on here. :)

Answer 6

ew... and I used skew twice too! and spelled slope as "slop". very descriptive of my word choice.. haha. well I suppose thats what I get for rushing xD

Answer 7

LOL

Answer 8

@Rylic234 disregard any mention to skew in my original answer! I was confusing myself with higher dimensions of geometry! Any time I wrote skew, replace it in your mind with "intersecting"!

Answer 9

So they have to come up with the equation of a line that will create the given system?

Answer 10

Ok :) Hey Rylic, how could you use your line, 3x + 5y = 7 to find the equation of a line that has no solutions?

Answer 11

Ah, wait! :D LifeEngineer came up with an equation of a parallel line ... so ... I am just making noise! :D

Answer 12

Ignore the anteater! ;)

Answer 13

Who will now wish you all a fine evening and go find something to snack on. :D G'night!!!

Answer 14

Gnight! Best of luck satiating your hunger!