1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linear System Question

  1. Jul 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm trying to solve #1 here:
    http://www.student.math.uwaterloo.ca/~math115/Exams/M115.FE.pdf [Broken]

    The problem is:

    3. The attempt at a solution
    (a) At a=2, the slope is the same. I figure any value but 2 gives unique solutions. But I don't know if this is right.
    (b) At a=2, the slopes are the same, but lines are different. I cannot find any value of a that would give the same slope and same outputs for inputs of x. DNE is the answer?
    (c) At a=2, there are no solutions for the system because the lines are parallel to each other. a=2 is the answer.
    (d) I think this part was done correctly. I used substitution and solved for the x and y values at a=1 and resulted with (2/3, 1/3)

    I would like to know about a, b, and c. I don't know if I did these right.

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jul 11, 2012 #2


    User Avatar
    Homework Helper

    Ignoring (a) and (b) for the moment:
    (d) is right, but (c) is wrong. At a = 2, you have this system:
    x + 2y = 1
    2x + 4y = 2
    Parallel lines have the same slope, but different y-intercepts. Is that the case here?
  4. Jul 11, 2012 #3


    User Avatar
    Science Advisor

    Hey JettyZ.

    For c), there are many solutions corresponding to x = t and y = 1 - 2t for any value of t.
    For a) and b) you need to use determinants and check for possibilities of inconsistent solutions.
  5. Jul 11, 2012 #4


    User Avatar
    Science Advisor

    If a= 2, your equations are x+ 2y= 1 and 2x+ 4y= 2. If you multiply the first equation by 2, what happens? What does that tell you?
  6. Jul 11, 2012 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Do you know about determinants and their relationship to such questions? If so, use a determinant; you will see that there is a critical value of 'a' that you have missed.

    Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook