Inconsistent equations and inequalities

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 

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, consistent and independent, 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. 

Related Terms for Inconsistent

  • Solution
  • Equation
  • Inequality

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