State whether the system is consistent and independent, consistent and dependent, or 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: 5x + 5z = 10 [Multiply the third equation by 5.]
2x - 5z = - 3
5x + 5z = 10
7x = 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.