College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.1 - Systems of Linear Equations: Substitution and Elimination - 8.1 Assess Your Understanding - Page 556: 52

Answer

The system is inconsistent.

Work Step by Step

$\left\{\begin{array}{lllll} 3x & -2y & +2z & =6 & \\ 7x & -3y & +2z & =-1 & /R_{2}=r_{2}-r_{1}\\ 2x & -3y & +4z & =0 & /R_{3}=r_{3}-2r_{1} \end{array}\right.$ ... Eliminate $z$ in eq. 2 and 3 $\left\{\begin{array}{lllll} 3x & -2y & +2z & =6 & \\ 4x & -y & & =-7 & \\ -4x & +y & & =-12 & /R_{3}=r_{3}+r_{2} \end{array}\right.$ ... Eliminate y in equation 3 $\left\{\begin{array}{lllll} 3x & -2y & +2z & =6 & \\ 4x & -y & & =-7 & \\ & & 0 & =-19 & \end{array}\right.$ The third equation is impossible - there are no solutions. The system is inconsistent.
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