Independent Equations and Inequalities
Definition of Independent Equations and Inequalities
Independent Equations: A system of equations with exactly one solution.
Video Examples: Solving Equations and Inequalities
Example of Independent Equations and Inequalities

The system of equations given below is independent.
x + y + 3z = 12
y + z =  4
z = 2
Solved Example on Independent Equations and Inequalities
Ques: State whether the system is consistent and independent, consistent and dependent, or inconsistent:
Choices:
A. InconsistentB. Consistent and independent
C. Consistent and dependent
D. Consistent
Correct Answer: B
Solution:

Step 1: [Multiply the third equation by 1/2 then,add this equation to the first
equation.]
Step 3: [Subtracting y =  2 in the second equation.]
Step 4: 5x + 5z = 10 [Multiply the third equation by 5.]
Step 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.
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