# Chapter 9 - Section 9.4 - Applications Involving Pairs of Linear Equations - Exercises - Page 338: 1

The pieces are 54 cm and 42 cm long.

#### Work Step by Step

Let x be the length of the longer piece and y be the length of the shorter piece. Together, the two pieces are 96 cm long, so: $x+y=96$ The longer piece is 12 cm longer, so: $x=y+12$ Substitute $y+12$ for $x$ in the first equation. $y+12+y=96$ $\longrightarrow$ simplify $2y+12=96$ $\longrightarrow$ subtract 12 from both sides $2y+12-12=96-12$ $\longrightarrow$ simplify $2y=84$ $\longrightarrow$ divide both sides by 2 $2y\div2=84\div2$ $\longrightarrow$ simplify $y=42$ Substitute 42 for y in the second equation. $x=42+12=54$

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