Are inconcistency equations always parallel?

Question:

Are inconcistency equations always parallel?

Solutions to System of Linear Equations:

In mathematics, a system of linear equations is a set of two or more equations that are both linear equations and have the same variables. The solution to a system of linear equations is equal to the point where all of the lines in the system intersect.

Answer and Explanation:

Yes, the lines with equations in a system of inconsistent linear equations are always parallel. An inconsistent system of equations is a system of equations that has no solution. By definition, the solution to a system of linear equations is the point where the lines in the system intersect. If a system of linear equations is inconsistent, then the lines in the system must not intersect. Otherwise, there would be a solution to the system. Two lines that never intersect are always parallel lines. Therefore, the lines with equations in a system of inconsistent linear equations are always parallel.


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Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
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