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!

2x + y = 8, x - z = 2. Solve by elimination and substitution

  1. Mar 2, 2014 #1


    User Avatar

    1. The problem statement, all variables and given/known data

    2x + y = 8, x - z = 2. Solve by elimination and substitution

    2. Relevant equations

    2x + y = 8, x - z = 2

    3. The attempt at a solution

    It cannot be solved by elimination or substitution.
    Last edited: Mar 2, 2014
  2. jcsd
  3. Mar 2, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You can solve for y and z in terms of x.
  4. Mar 3, 2014 #3
    To add to LCKurtz's response, you have two equations with three variables. You can solve for any of the following:

    • [itex]x[/itex] and [itex]y[/itex] in terms of [itex]z[/itex]
    • [itex]x[/itex] and [itex]z[/itex] in terms of [itex]y[/itex]
    • [itex]y[/itex] and [itex]z[/itex] in terms of [itex]x[/itex]
    But you cannot solve for all three.
  5. Mar 3, 2014 #4


    User Avatar
    Science Advisor

    What I would do is say that, from the first equation, y= 8- 2x, and from the second equation, z= x- 2.

    That is, any (x, y, z) satisfying these equations is of the form (x, 8- 2x, x- 2).

    Or if you prefer "parametric equations", (x, y, z) satisfies those equation if and only if x= t, y= 8- 2t, and z= t- 2. Those points lie on a straight line in "three-space". Geometrically, a line is determined by two points. This line is the line that passes through (0, 8, -2) and (2, 4, 0).
  6. Mar 3, 2014 #5
    Oops! My "correction" was erroneous.

    Last edited: Mar 3, 2014
  7. Mar 3, 2014 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Everything HallsofIvy said was 100% correct. Where do you think he was wrong?
  8. Mar 3, 2014 #7
    Correct. Sorry to both you and HoI.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted