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AssignmentMultiple Choice

Solving 3 x 3 Linear Systems

Question 2 • OK-Algebra II A

Which of the following systems is possible?

Answer
A
a system of two linear equations with exactly two solutions
B
a system of two linear equations that is consistent and has no solutions
C
a system of two linear equations that is dependent and has exactly one solution
D
a system of two linear equations that is independent and has no solutions

Explanation

Two linear equations are independent when they represent distinct lines. Distinct parallel lines never intersect, so their system has no solution; therefore an independent system with no solutions is possible. The other descriptions conflict with the standard cases: two lines cannot intersect at exactly two points, and a consistent system must have at least one solution.

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