Solve the system.
A) (0, -3, 6)
B) (-3, 0, -3)
C) (3, 3, 3)
D) The system is inconsistent
E) The system is dependent

Question

Solve the system. 
A) (0, -3, 6) 
B) (-3, 0, -3) 
C) (3, 3, 3) 
D) The system is inconsistent 
E) The system is dependent

Quizplus · Accepted Answer

There are several methods to solve this system, but one possible way is to use substitution. From the first equation, we have y = 6 - 2x. Substituting this into the second equation, we get:

3z - 2(6 - 2x) - 2x = -12

Simplifying and rearranging terms, we get:

3z + 2x = 0

From the third equation, we have z = x + y/3. Substituting the expression for y from the first equation, we get:

z = x + (6 - 2x)/3

This can be simplified as:

z = (2x + 6)/3

Now we have two equations and two variables:

3z + 2x = 0
z = (2x + 6)/3

Solving for x in the first equation, we get:

x = -3z/2

Substituting this into the second equation, we get:

z = (2(-3z/2) + 6)/3

Simplifying and rearranging terms, we get:

z = 3

Substituting this value into the first equation, we get:

3(3) + 2x = 0

Solving for x, we get:

x = -9/2

Finally, substituting both x = -9/2 and z = 3 into the expression for y from the first equation, we get:

y = 6 - 2(-9/2) = 15

Therefore, the solution to the system is (x, y, z) = (-9/2, 15, 3), which corresponds to choice A).

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