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 539: 35

Answer

$x=3.5$ $y=1.5$ $z=0.75$

Work Step by Step

We will denote price of a gallon of milk by $x$, price of bottle of water by $y$ and price of snack-size bag of chips by $z$. We are given the system: $\begin{cases} 2x+5y+6z=19\\ y=2z\\ x=y+2 \end{cases}$ We substitute $y$ in places of $2z$ in the first equation. and substract $y$ from both sides in the second equation to get the variables on one side of the equation. $\begin{cases} 2x+5y+3(2z)=2x+5y+3y=2x+8y=19\\ x-y=y-y+2=x-y=2 \end{cases}$ We will use the addition method. Multiply the Equation 2 by $8$ and add it to Equation 1. $\begin{cases} 2x+8y=19\\ 8x-8y=16 \end{cases}$ $10x=35$ $x=3.5$ Substitute the value of $x$ in the Equation $x=y+2$ to determine $y$: $3.5=y+2$ $1.5=y$ Substitute the values of $x, y$ in Equation 1 of the given system to find $z$: $2x+5y+6z=19$ $2(3.5)+5(1.5)+6z=19$ $7+7.5+6z=19$ $6z=19-14.5$ $z=0.75$ The solution is $(x=3.5,y=1.5,z=0.75)$
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