Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation.
A) (-2, -1, 3)
B) (-z + 1, -z + 2, z)
D) no solution, inconsistent

Question

Solve using the elimination method. If the system is inconsistent or dependent, so state. For a system with linear dependence, write the answer in terms of a parameter. For coincident dependence, state the solution in set notation. 
A) (-2, -1, 3) 
B) (-z + 1, -z + 2, z) 
D) no solution, inconsistent

Quizplus · Accepted Answer

Using elimination method, we can eliminate x by adding the first and second equations:
2x + y -z = 12
2x + 2y + z = 24
------------
3y = 12
y = 4
Substitute y into first equation and solve for x:
x - 2(4) + 3z = 10
x + 3z = 18
Substitute y and x into third equation and solve for z:
2(-2) + 2(4) - z = 0
-z = -4
z = 4
Thus we have the solution (x,y,z) = (14, 4, 4), which is not dependent or inconsistent. Therefore, choice C is the best answer.

Solve Using the Elimination Method