College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.2 - Page 537: 15


$\{ (1,-5,-6) \}$

Work Step by Step

Plan (see p.533): 1. Eliminate one variable and arrive at a system of two equations in two variables. 2. Solve the system of two equations in two variables. 3. Back-substitute the solutions of (2) to find the eliminated varable in (1) ------------ (1.) Perform elimination by addition method (eliminate z) by $Eq.$2 already is without x. $-2Eq.1+Eq.3 \Rightarrow$ $(-2+2)x+(1-2)y+(3-0)z=-21+8$ $\left[\begin{array}{ll} y-z=1 & I\\ -y+3z=-13 & II \end{array}\right.$ , ({\it 2}.) ... $I+II$ eliminates $y$: $2z=-12$ $z=-6$ Back-substitute into $y-z=1$ $y-(-6)=1$ $y=1-6$ $y=-5$ (3.) Back-substitute into one of the initial equations: $x+y=-4$ $x-5=-4$ $x=1$ Solution set: : $\{ (1,-5,-6) \}$
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