Question

is the system consistent or inconsitent?
2x+3y=5
4x+6y=19

Answer 1

Do you know what consistent and inconsistent mean?

Answer 2

no

Answer 3

Ok. Consistent means that there is at least one solution, and inconsistent means that there is no solutions.

Answer 4

oh okay. how do i figure out the solution ?

Answer 5

Well...there might be an easier way to do this, but what I would do is change both lines to the slope-interept form of a line, and then if they have the same slope, they will never have a solution and thus be inconsistent. (unless they're the same line...then there is infinite solutions) But if they are not the same slope, they would have to intercept sometime, so they'd be consistent.

So let's change these lines to the slope-intercept form.
2x +3y = 5 ---First line
3y = -2x + 5
y = -2/3x + 5/3

4x+6y=19 --Second line
6y=-4x+19
y=-4/6x+19/6
y = -2/3x + 19/6

Here you can see that they have the same slope, but different y intercepts, so they are parallel and thus inconsistent. :)

Answer 6

thanks (:

Answer 7

No problem.