Solve the system of equations by graphing. Then classify the system. 9x - 5y = -30 and 5y - 9x = 30. What is the ordered pair? Is this consistent or inconsistent? Dependent or Independent?

Question

Solve the system of equations by graphing.  Then classify the system.  9x - 5y = -30 and 5y - 9x = 30.  What is the ordered pair?  Is this consistent or inconsistent?  Dependent or Independent?

hero · Answer

Solve both equations for y first

hero · Answer

Wait a second, everything cancels

hero · Answer

0x + 0y = 0

means infinite solutions

hero · Answer

If you graphed both you would get the same line and infinite ordered pairs

anonymous · Answer

okay, that makes sense.  So would it be inconsistent and dependent?

hero · Answer

Well, they're both independent lines. Neither depends on the other because each can exist by themselves.

hero · Answer

They're consistent in the sense that they both have the same ordered pairs infinitely

hero · Answer

They have the same slope as well

anonymous · Answer

Okay, that also makes sense.

hero · Answer

In fact, they're both the same exact graph

anonymous · Answer

So it would be one line over the top of the other??

hero · Answer

No, they're both the same line, meaning it's not one on top of the other...they're just the same exact line

anonymous · Answer

But it looks like just one line, right?

hero · Answer

It IS one and only one line

anonymous · Answer

okay, great.  That helps.

hero · Answer

Well, I guess you can say one on top of the other since if you graph it, you're only graphing the same line twice.

hero · Answer

The two graphs occupy the same space at the same time...that's a little more accurate to say

anonymous · Answer

got it.