SOLUTION: Solve the system of equations by the Gaussian elimination method. (If the system is dependent, enter a general solution in terms of c1, c2, ... 3x − 5y + 2z = 2 x &#8722

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations by the Gaussian elimination method. (If the system is dependent, enter a general solution in terms of c1, c2, ... 3x − 5y + 2z = 2 x &#8722      Log On


   

Question 632158: Solve the system of equations by the Gaussian elimination method. (If the system is dependent, enter a general solution in terms of c1, c2, ...
3x − 5y + 2z = 2
x − 3y + 2z = 2
5x − 11y + 6z = 6
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

3x − 5y + 2z = 2

 x − 3y + 2z = 2

5x − 11y + 6z = 6

Dependent system as D =0, as well as Dx=0, Dy= 0 and Dz = 0

or as demonstated by selecting different pairs of EQs and eliminating z for both: 

2x - 2y = 0

2x - 2y = 0    |Subtracting 2nd from 1st

     0 = 0   Dependent System

Dependent relationship in terms of z: (z-1, z-1, z)

 x = z - 1     |Eliminating y-variable using a pair of EQs

 y = z - 1     |Eliminating x-variable using a pair of EQs