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A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a syste be consistent? Illustrate your answer with a specific system of three equations in two unknowns. Choose the correct answer below. O A. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, x₂ = 4, X₁ +X₂ = 8 O C. No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution. x₁ = 2, x₂ = 4, x₁ +X₂ = 24 O B. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, x₂ = 4, x₁ +X₂ = 6 OD. No, overdetermined systems cannot be consistent becaus there are fewer free variables than equations. For exampl the system of equations below has no solution. x₁ = 2, x₂ = 4, X₁ + X₂ = 12

A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a syste be consistent? Illustrate your answer with a specific system of three equations in two unknowns. Choose the correct answer below. O A. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, x₂ = 4, X₁ +X₂ = 8 O C. No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution. x₁ = 2, x₂ = 4, x₁ +X₂ = 24 O B. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, x₂ = 4, x₁ +X₂ = 6 OD. No, overdetermined systems cannot be consistent becaus there are fewer free variables than equations. For exampl the system of equations below has no solution. x₁ = 2, x₂ = 4, X₁ + X₂ = 12

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.1: Systems Of Linear Equations
Problem 101E
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A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. Choose the correct answer below. O A. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, X₂ = 4, x₁ + x₂ = 8 O B. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, X₂ = 4, x₁ + x₂ = 6 OC. No, overdetermined systems cannot be consistent because O D. No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of there are fewer free variables than equations. For example, equations below has no solution. the system of equations below has no solution. x₁ = 2, X₂ = 4₁ x₁ + x₂ = 24 x₁ = 2₁ X₂ = 4₁ x₁ + x₂ = 12
Transcribed Image Text:A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. Choose the correct answer below. O A. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, X₂ = 4, x₁ + x₂ = 8 O B. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (Type an ordered pair.) x₁ = 2, X₂ = 4, x₁ + x₂ = 6 OC. No, overdetermined systems cannot be consistent because O D. No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of there are fewer free variables than equations. For example, equations below has no solution. the system of equations below has no solution. x₁ = 2, X₂ = 4₁ x₁ + x₂ = 24 x₁ = 2₁ X₂ = 4₁ x₁ + x₂ = 12
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