Need help with a simultaneous equation question..

[Slumdawg]

The simultaneous linear equations,

2x +py = 3q

3x + qy = 2p

where p and q are real constants, have a unique solution provided, as follows:

A. p = 2q/3

B. p [does not equal, equals sign with a diagonal line through it] 2q/3

C. p = 3q/2

D. p [does not equal] 3q/2

E. p = -3q/2

Please show workings Thanks.

[vea]

NOTE:This question isn't really a simultaneous equation.

If the two linear equations are to have unique solutions, then the two equations cannot be:

1. The same line or else the two equations will have infinite many solutions.
2. Parallel to each other or else the equations will have no solutions.

In both cases we want to make sure that the gradient of both equations are not equal.

Equation 1:




Equation 2:




So for the gradients to not be equal.







So the correct answer is B

[luken93]

Answer is B

care to explain? I'm not sure about it either?

[stonecold]

It is stupid parameter stuff.  Is this in the course?  It is in the textbook I know that.

I've never really gotten it...

[Slumdawg]

It is stupid parameter stuff.  Is this in the course?  It is in the textbook I know that.

I've never really gotten it...

Oh god. If you don't get it what hope do the rest of us have..

Its from a neap paper. Sometimes they get a bit carried away..

[Slumdawg]

NOTE:This question isn't really a simultaneous equation.

If the two linear equations are to have unique solutions, then the two equations cannot be:

1. The same line or else the two equations will have infinite many solutions.
2. Parallel to each other or else the equations will have no solutions.

In both cases we want to make sure that the gradient of both equations are not equal.

Equation 1:




Equation 2:




So for the gradients to not be equal.







So the correct answer is B

Well done! That does make sense. Thanks heaps.

[luken93]

It is stupid parameter stuff.  Is this in the course?  It is in the textbook I know that.

I've never really gotten it...

Oh god. If you don't get it what hope do the rest of us have..

Bahaha calm down I'm not that good!

[luken93]

NOTE:This question isn't really a simultaneous equation.

If the two linear equations are to have unique solutions, then the two equations cannot be:

1. The same line or else the two equations will have infinite many solutions.
2. Parallel to each other or else the equations will have no solutions.

In both cases we want to make sure that the gradient of both equations are not equal.

Equation 1:




Equation 2:




So for the gradients to not be equal.







So the correct answer is B

Well done! That does make sense. Thanks heaps.

I was actually just about to arrange it to make it y =
but you've done it anyway, oh well!

[stonecold]

It is stupid parameter stuff.  Is this in the course?  It is in the textbook I know that.

I've never really gotten it...

Oh god. If you don't get it what hope do the rest of us have..

Its from a neap paper. Sometimes they get a bit carried away..

Oh, it was actually easy haha.  But yeah, I still don't really get parameters.  I'll see what q's I can find on them.

[iffets12345]

Um, I don't know if you learn this in CAS, but it's much simpler with matrices... and the determinent.

|2  p | |x| = |3q|
|3  q | |y| = |2p|

The system will have no unique solution if the determinent is zero. 2q-3p = 0
p does not equal, 2q/3

[TrueTears]

It is stupid parameter stuff.  Is this in the course?  It is in the textbook I know that.

I've never really gotten it...

Definitely in the course, actually this is not the parameter stuff, but I do know what you are talking about, the parameter stuff follows this immediately in Essentials methods 3/4 but actually doesn't relate much to this question.