Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Practice: 1

Answer

2$x$- $y$ + 3$z$ =13 $x$ + $y$ - $z$ = -2 3$x$ + 2$y$ + 2$z$ = 13 (1, 1, 4) $x$ = 1 $y$ = 1 $z$ = 4

Work Step by Step

Step 1: Write Out Problems 2$x$- $y$ + 3$z$ =13 (equation 1) $x$ + $y$ - $z$ = -2 (equation 2) 3$x$ + 2$y$ + 2$z$ = 13 (equation 3) Step 2: Find the 2 equations with like terms (in this case $y$), and cancel out the like terms 2$x$- $y$ + 3$z$ =13 $x$ + $y$ - $z$ = -2 ----------------------- 3$x$ + 2$z$ = 11 (equation 4) Step 3: Add two $other$ equations and eliminate $y$ again 2(2$x$- $y$ + 3$z$) =13 (2) 3$x$ + 2$y$ + 2$z$ = 13 Simplify: $4x$- $2y$ + $6z$ = 26 3$x$ + 2$y$ + 2$z$ = 13 ____________________ $7x$ + $8z$ = 39 (equation 5) Step 4: Combine equations 4 and 5, and multiply equation 4 by -4 -4 ($3x$ + $2z$) = 11 (-4) $7x$ + $8z$ = 39 Simplify: $-12x$ -$8z$ = -44 $7x$ + $8z$ = 39 $-5x$ = -5 $x$ = 1 Now replace $x$ with 1 3(1) + $2z$ = 11 $2z$ = 8 $z$ = 4 Solve: for $y$ $x$ + $y$ - $z$ = -2 1 + $y$ - 4 = -2 $y$ -3 = -2 $y$ = 1
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