Question

Please help!

The following system of equations is _____.

y = -1/3x + 2/3
2x + 6y = 4

is it inconsistent??


independent
equivalent
inconsistent

Answer 1

Have you considered putting both equations into standard form, like the second one, and comparing them?

Answer 2

@tkhunny yes i got 1/3x + y= 2/3

Answer 3

That's a good start. Multiply it by 3. "Standard Form" usually asks for integer coefficients if it is possible.

Answer 4

then it would be x+3y=2?

Answer 5

Yes. Remember that any equations that are multiples of each other are equal.

Answer 6

Okay,

x + 3y = 2
2x + 6y = 4

Why not make your life simpler and remove the common factor from the second equation? Divide everything by 2.

Answer 7

oh then it will be parallel!! inconsistent right??

Answer 8

No.

These two are parallel and inconsistent.

x + 3y = 2
x + 3y = 3

There are no solutions.

These two are EXACTLY the Same. This makes them consistent, but annoying.

x + 3y = 2
x + 3y = 2

There are infinitely many solutions.

Answer 9

ohhhh darn ): thanks for the help though! do you mind answering another question for me?

Answer 10

gtg to my real job. Sorry. @slickwilly might still be around.