Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

Show Tags

13 Apr 2007, 02:51

5

This post received KUDOS

3

This post was BOOKMARKED

A system of linear equations with a unique solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.
So we have to find out the the value K so that the lines become parallel. Parallel lines don't intersect each other. That's why having no unique solution.

Two parallel lines have their slopes equal.
Slope of the line 3x+4y = 12, = -3/4

Putting K =9 in the line kx+12y = 30 , slope of this line = -3/4

Hence for k =9 the second line is parallel to the first one. Hence the lines will not have a unique solution.

For 2 equations of line, we have 3 possible cases:
> 1 point intersect the 2 lines = 2 different slopes for the lines
> No intersection = Same slopes and different Y-interceptors
> Infinite number of interesections = Same slopes and same Y-interceptors

So, the question just asks us for which value of k, the slopes are equal.

o 3x+4y = 12
<=> y = -3/4 * x + 12

o kx+12y = 30
<=> y = -k/12 * x + 30/12

By equalizing the 2 slopes, we have:
-k/12 = -3/4
<=> k = 12*3/4 = 9

The pairs will not have a unique solution if the lines are parallel. To find this, just make sure both lines have similar slopes. Above, I have place the equations in the standard straight-line equation y = mx+c where m is the gradient of the line and c is the y-intercept.

so since y = -0.5x+3 has a gradient of -0.5, then we must make sure y = kx/12+2.5 has a gradient of -0.5 too. To have this, we need k = 9.

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

Show Tags

09 Jan 2012, 00:47

Hi Guys, let me know if this approach is correct(its a shortcut though):) solving the two eq simultaneously, we get kx-9x=18 so for any value except 9 for K we ill have a unique solution. so 9 is our answer.

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

Show Tags

24 Sep 2015, 10:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...