SOLUTION: x1 + 2x2 + 6x3 = 6 x1 + x2 + 3x3 = 3 (x1, x2, x3) =

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Question 1108012: x1 + 2x2 + 6x3 = 6
x1 + x2 + 3x3 = 3
(x1, x2, x3) =

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given this system of two equations

 x1 + 2x2 + 6x3	 = 6    (1)
 x1 +  x2 + 3x3	 = 3    (2)


Multiply eq(2) by 2 (both sides).  Keep eq(1) as is.  You get an EQUIVALENT system

 x1 + 2x2 + 6x3	 = 6    (3)
2x1 + 2x2 + 6x3	 = 6    (4)


Next, subtract eq(3) from eq(4)  (both sides).  You will get  x1 = 0.


So, you just found x1, and you can exclude this variable from the system.


Then, due to (3),(4),  you have these two equations instead (3),(4)

     2x2 + 6x3 = 6,     (5)
     2x2 + 6x3 = 6.     (6).


These two equations are IDENTICAL,  so, you actually have ONE single equation for two unknowns x2  and  x3.


It has INFINITELY MANY solutions.  You can take x3 by an arbitrary way, and then get x2 = 3 - x3.


Hence, the original system has infinitely many solutions

    x1= 0,  x3  is ARBITRARY,  and  x2 = 3 - x3.

Solved.