Expert: Paul Klarreich - 3/17/2009

Question
hOW WOULD YOU SOLVE r+s+t=5, 2r-7s-3t=13, and 1/2r - 1/3s+2/3t=-1, in Algebra 2, which is called Solving Systems of Equations With Three Variables? Please help cause this one has me a lil stuck.

Answer
Questioner:   Andre
Category:  Advanced Math
Private:  No
 
Subject:  Algebra 2
Question:  hOW WOULD YOU SOLVE r+s+t=5, 2r-7s-3t=13, and 1/2r - 1/3s+2/3t=-1, in Algebra 2, which is called Solving Systems of Equations With Three Variables? Please help cause this one has me a lil stuck.
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You start by fixing your keyboard, then making your equations look nice.  The nicer they look, the better you will understand them.  (I am not kidding.)

 r +  s +  t =  5       (A)
2r - 7s - 3t = 13   (B)
1/2r - 1/3s + 2/3t = -1  (C)

See how the spacing and lining up makes it easier to see?

Now that you see them, it should occur to you to clear fractions in C.  You are in algebra 2, so I assume you know how to do that.

 r +  s +  t =  5     (A)
2r - 7s - 3t = 13     (B)
3r - 2s + 4t = -6     (C)

Now you can get to work.  If you know how to solve TWO equations, then you know this, too.  Simply pick one of the variables, and eliminate it from the sytem.  I shall pick 't'.  [After you do 3-4 hundred of these, you'll know how to pick it.]


3r + 3s + 3t = 15    (3A)
2r - 7s - 3t = 13     (B)
----------------------    add
5r - 4s      = 28    << no t.

-4r - 4s - 4t =-20    (-4A)
3r - 2s + 4t = -6     (C)
-----------------------------
-1r - 6s      = -26


5r - 4s      = 28    << no t.
-1r - 6s      = -26   << no t.

You can handle the rest.