State whether the system is consistent and independent, consistent and dependent, or inconsistent:

**Choices:**

A. Inconsistent

B. Consistent and independent

C. Consistent and dependent

**Correct Answer: B**

**Step 1:** [Multiply the third equation by
then, add this equation to the first equation.]

**Step 2: ***y* = - 2 [Solve for *y*.]

**Step 3:** [Subtracting *y* = - 2 in the second equation.]

**Step 4:** 5*x* + 5*z* = 10 [Multiply the third equation by 5.]

**Step 5:**

2*x* - 5*z* = - 3

__5__*x* + 5*z* = 10

__7__*x* = 7 [Add.]

**Step 6:** *x* = 1 [Solve for *x*.]

**Step 7:** *x* + *z* = 2 implies 1 + *z* = 2 implies *z* = 1. [Substitute the values.]

**Step 8:** The solution is (1, -2, 1).

**Step 9:** The system is consistent and independent, it has only one real solution.