Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises: 39

Answer

$r = 4$, $s = 1$

Work Step by Step

Given: $r + 3s = 7$ $2r - s = 7$ Multiply the first equation, $r + 3s = 7$, by $2$: $2r + 6s = 14$ Subtract the second equation, $2r - s = 7$, from the first, $2r + 6s = 14$: $2r + 6s - (2r + -s) = 14 - (7)$ $2r - 2r + 6s - (-s) = 7$ $6s + s = 7$ $7s = 7$ Divide both sides by $7$: $s = 1$ Substitute $s = 1$ into the first equation, $r + 3s = 7$. $r + 3s = 7$ $r + 3(1) = 7$ $r + 3 = 7$ Subtract $3$ from both sides: $r = 4$ $r = 4$, $s = 1$
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