Question

Does anybody know how to do this?
The lines 4x-2y=6 and 5y=10x-15 intersect in how many points? (And how do you find the answer?)

Answer 1

hint: solve each equation for y

Answer 2

oh, ok
wait, but do u know what the answer is?

Answer 3

What do you get when you solve 4x-2y=6 for y?

Answer 4

um, you get 2x-6

Answer 5

Close

4x - 2y = 6

-2y = -4x + 6

y = (-4x + 6)/(-2)

y = (-4x)/(-2) + 6/(-2)

y = 2x - 3

Answer 6

What do you get when you solve 5y=10x-15 for y?

Answer 7

y=2x-3

Answer 8

So 4x-2y=6 and 5y=10x-15 are the same equation because solving for y yields y = 2x - 3


The same equation produces the same graph, so the two lines coincide. One line lies right on top of the other. So there are infinitely many points of intersection which means there are infinitely many solutions.

Answer 9

4x - 2y = 6 reduces to 2x - y = 3

5y = 10x - 15
-10x + 5y = -15-->(-1)
10x - 5y = 15 reduces to 2x - y = 3

as you can see, when broken down, they have the same line. Therefore, there are infinite solutions

Answer 10

This system is consistent (there is at least one solution) and it's dependent (one equation depends on the other...ie one is a scalar multiple of the other)

Answer 11

oh so the answer is many solutions?

Answer 12

infinitely many, yes

Answer 13

oh, thank-you

Answer 14

np