Determine whether the system is inconsistent, dependent, or neither.
-3x + y = 8 -4y - 3z = -29
3x + 5y + 3z = 37
A) dependent
B) inconsistent
C) neither

Question

Quizplus · Accepted Answer

We can solve for x in terms of y and z by rearranging the first equation: 
3x + y = 8 
3x = 8 - y 
x = (8 - y)/3

Then we can substitute this expression for x into the second and third equations: 
-4y - 3z = -29 becomes 
-4y - 3z = -29 - (8 - y) 
-4y - 3z = -37 + y

3x + 5y + 3z = 37 becomes 
(8 - y) + 5y + 3z = 37 
-y + 3z = 5

Now we have two equations in two variables (-4y - 3z = -37+y and -y + 3z = 5) which we can solve using elimination or substitution. We find that y = -2 and z = 1. Substituting these values back into the first equation, we find x = 2. Therefore, the system has infinitely many solutions and is dependent.

Determine Whether the System Is Inconsistent, Dependent, or Neither