Determine whether the system is consistent, in consistent, or dependent.
3x + 2y = 15
6x + 4y = 30

Question

Determine whether the system is consistent, in consistent, or dependent.
3x + 2y = 15
6x + 4y = 30

anonymous · Answer

http://www.sparknotes.com/math/algebra1/systemsofequations/section1.html

anonymous · Answer

"If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.

If the two equations describe lines that intersect once, the system is independent and consistent.

If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent."

mertsj · Answer

The two equations are exactly the same equation.  The graph is, of course, a line.  So every point on the line is a solution of the equation.  Since a line consists of an infinite number of points, there is a infinite number of solutions.  Such a system is called consistent and dependent.

anonymous · Answer

Okay not sure I got it but with work with what you have both given me, including the web info.

anonymous · Answer

Okay think about it this way:  That first eqn is just 2*(3x + 2y = 15)

So equation 2 is just a multiple of equation 1.  

To show that they're the same, just get both of them in slope-intercept form.  y=mx+b and the graph both of them.  Just to prove it to yourself :-)

anonymous · Answer

okay I will give that a try thank you brinethery :)

anonymous · Answer

eqn 1:  y = -3x/2 +15/2

eqn 2: y= -6x/4 +30/4.  Reducing it gives: y=-3x/2 +15/2

Check!

anonymous · Answer

Thank you brinethery, I still am not sure if this is consistent, inconsistent or dependant. Trying to grasp it.

anonymous · Answer

You've got two lines that are sitting on top of one another (3rd pic) http://img.sparknotes.com/figures/A/ae9daa68f8a4f991e2068793c87afedc/system_graphs.gif Meaning: Consistent and dependent

anonymous · Answer

okay, thank you.

anonymous · Answer

So for these, the first step is to always always always getting both of your lines in the form y=mx+b.  If you have any fractions for m and b, see if they can be reduced further.

It's also a very good idea to graph them both on paper to see for yourself.

And try to memorize that picture with the three graphs (the third graph has two lines but they're on too of one another.)

anonymous · Answer

okay I will give your advice a try to see how it looks.