Determine whether the system of linear equations is inconsistent or dependent.

Question

Determine whether the system of linear equations is inconsistent or dependent.

	−2x	+	6y	−	2z	=	−18
x	−	3y	+	2z	=	14
−x	+	3y	+	2z	=	6

inconsistentdependent    

If it is dependent, find the complete solution. (If the system is dependent, express your answer in terms of t, where x = x(t),

 y = t,

 and z = z(t).

 If the system is inconsistent, enter INCONSISTENT.)

(x, y, z) =

Answer 1

Adding the 2nd and 3rd equations:

4z = 20 ---> z = 5

the system becomes: -2x + 6y - 10 = -18 ---> -2x + 6y = -8

x - 3y + 10 = 14 ---> x - 3y = 4

x + 3y + 10 = 6 ---> x + 3y = -4

adding the 2nd and 3rd of these equations gives: 2x = 0 ---> x=0

the system becomes:

6y = -8 ----> y = -4/3

-3y = 4 ---> y = -4/3

3y = -4 --> y = -4/3

the solution is {x=0, y = -4/3, z = 5}

yes it checks