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 - Got It? - Page 374: 3


$5$ new games were rented.

Work Step by Step

Step $1$ Write the system of equations. Let x = number of old games, y = number of new games. You rented 6 video games:$\quad x+y=6$ The cost was $ {{\$}} 22:\qquad 2x+4y=22$ Step $2$ Solve one of the equations for one of the variables. $x+y=6\quad\Rightarrow\quad y=6-x$ Step $3$ Substitute $6-x$ for $y$ in the other equation and solve for $x$ $2x+4y=22$ $2x+4(6-x)=22\quad $... simplify $ 2x+24-4x=22\quad$ ... subtract 24 $-2x=-2\quad $... divide with -2 $x=1$ Step $4$ Substitute $1$ for $x$ in$\quad x+y=6 \quad $and solve for $y$. $y+1=6$ $y=5$ Reverting back to the meaning of x and y, 1 old game was rented, and $5$ new games were rented.
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