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The two lines drawn from a system are parallel and never meet, however far they are extended. What does that say about the system?
AIt is dependent and has many solutions
BIt is independent and has one solution
CIt is consistent and has one solution
DIt is inconsistent and has no solution
Answer & Solution
Correct answer: D. It is inconsistent and has no solution
1. A solution has to be a point that lies on both lines at once.
2. Parallel lines share no point at all, so no such pair exists.
3. A system with no solution is called inconsistent.
4. So the system is inconsistent with no solution, option D.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_
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