Section 3.6 Systems of Linear Equations in Three Variables and Applications 289 Answers 4. Infinitely many solutions; dependent equations 5. No solution; inconsistent system 2x y 2z 3 4x 2y 4z 6 x 2y 3z 5 x 2y 3z 5 5x z 11 5x z 11 5x z 11 5x z 11 2x 3y 7z 4 4x 6y 14z 1 5x y 3z 6 Multiply by 2. B x y z 8 2x y z 6 B C Solving an Inconsistent System of Linear Equations Solve the system. If the system does not have one unique solution, state the number of solutions and whether the system is inconsistent or the equations are dependent. Solution: We will eliminate the x variable from equations and . A (contradiction) 4x 6y 14z 8 4x 6y 14z 1 The result 0 9 is a contradiction, indicating that the system has no solution. The system is inconsistent. Skill Practice 5. Solve the system. If the system does not have one unique solution, state the number of solutions and whether the system is inconsistent or the equations are dependent. x 2y z 5 x 3y 2z 7 2x 4y 2z 6 0 9 2x 3y 7z 4 4x 6y 14z 1 A B Example 5 Multiply by 1. E Because equations and are equivalent equations, it appears that this is a dependent system. By eliminating variables we obtain the identity The result 0 0 indicates that there are infinitely many solutions and that the equations are dependent. Skill Practice Solve the system. If the system does not have one unique solution, state the number of solutions and whether the system is inconsistent or the equations are dependent. 4. 5x 2y 4z 30 0 0 D E 0 0. D E 5x z 11 B C Multiply by 2. Pair up equations and to eliminate y.
miller_intermediate_algebra_4e_ch1_3
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