Determine whether the system is inconsistent, dependent, or neither.
-x + y + z = 8 x - y + 5z = 4
2x + 2y + 2z = 11
A) inconsistent
B) dependent
C) neither

Question

Quizplus · Accepted Answer

This system is inconsistent because the third equation is a multiple of the first equation (dividing by 2 on both sides), but the second equation does not fit the pattern. Inconsistent systems have no solution. We can solve this system by using elimination method. First, we can subtract the first equation from the second equation to eliminate y:

x + y + z = 8
x - y + 5z = 4
----------------
-2y - 4z = -4

Next, we can divide the third equation by 2 to simplify the system:

x + y + z = 8
x - y + 5z = 4
x + y + z = 5.5

Now, we can subtract the third equation from the first equation to eliminate y:

0 = 2.5

This equation is not true, which means the system has no solution. Therefore, it is inconsistent.

Determine Whether the System Is Inconsistent, Dependent, or Neither