INCONSISTENT
Definition Of Inconsistent
Inconsistent Equations: A system of equations that has no solutions. .
Inconsistent inequalities:A system of inequalities that has no solutions.
Examples of Inconsistent
Inconsistent equations: The system of equations given below is inconsistent.
4x - 5y = 7
8x - 10y = 7
Inconsistent inequalities: The system of inequalities given below is inconsistent.
x - y ≤ 0
x - y ≥ 7
Video Examples:Consistent and Inconsistent Systems
Solved Example on Inconsistent
Determine whether the system of equations
0.5x - 0.3y = 1.2
1.5x - 0.9y = 2.1
is consistent and dependent, or inconsistent.
Choices:
A. inconsistent
B. consistent and independent
C. consistent and dependent
D. consistent
Correct Answer: A
Solution:
Step 1: 0.5x - 0.3y = 1.2 [Equation 1.]
Step 2: 1.5x - 0.9y = 2.1 [Equation 2.]
Step 3: 
[Rearrange equation 1 in slope-intercept form.]
Step 4: 
[Simplify.]
Step 5: 
[Rearrange equation 2 in slope-intercept form.]
Step 6: 
Step 7: Graph the equations.
Step 8: The two lines are parallel.
Step 9: So, the linear system has no solution
Step 10:Therefore, the system is inconsistent
Quick Summary
- Inconsistent equations represent parallel lines when graphed.
- Inconsistent inequalities represent regions that do not overlap when graphed.
🍎 Teacher Insights
Emphasize the graphical representation of inconsistent systems to provide a visual understanding. Use real-world examples where conflicting constraints lead to no feasible solution.🎓 Prerequisites
- Linear Equations
- Graphing Linear Equations
- Solving Equations
- Inequalities
Check Your Knowledge
Q1: Which of the following systems is inconsistent?
Frequently Asked Questions
Q: How can you tell if a system is inconsistent?
A: When solving, you arrive at a contradiction (e.g., 0 = 1). Graphically, the lines are parallel (for equations) or the regions don't overlap (for inequalities).
Q: Does an inconsistent system have any solutions?
A: No, an inconsistent system by definition has no solution.