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:
B. Consistent and independent
C. Consistent and dependent
Correct Answer: B
Step 1: [Multiply the third equation by then,-1/2add 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.]
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.