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## 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.

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

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