Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Practice and Problem-Solving Exercises - Page 376: 32


System: $\left\{\begin{array}{l} l=5+2w\\ 2l+2w=34 \end{array}\right.$ Width: $w=4$ cm Length: $l=13$ cm

Work Step by Step

$l$ is 5 more than 2$\times$w $\qquad \Rightarrow\qquad l=5+2w$ Perimeter = 34 $\qquad \Rightarrow\qquad 2l+2w=34$ Substitute $5+2w$ for $l$ in the second equation and solve for $w$ $ 2(5+2w)+2w=34 \quad$ ... distribute, simplify $ 10+4w+2w=34 \quad$ ... add $-10$ $ 6w=24\quad$ ... divide with $3$ $w=4$ cm Substitute $4$ for $w$ in $\qquad l=5+2w$ $l=5+2\cdot 4=13$ cm Width: $w=4$ cm Length: $l=13$ cm System: $\left\{\begin{array}{l} l=5+2w\\ 2l+2w=34 \end{array}\right.$ Width: $w=4$ cm Length: $l=13$ cm Check: The area is 13(4)=52.
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