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

Question

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

	x	+	y	+	z	=	4
y	−	3z	=	11
2x	+	y	+	5z	=	−5

dependentinconsistent    

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 = y(t),

 and z = t.

 If the system is inconsistent, enter INCONSISTENT.)

(x, y, z) =

 

 

Answer 1

y+3z = 11

2x + y + 5z = -5

x+y +z =4

x=-23/3 =- 7 2/3

x= -7 2/3

y - 12

z = -1/3

solved by matrix algebra or by substitution and elimination. the 3 equations in 3 unknown variables are linearly independent, not contradictory and have a unique solution.