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: 40

Answer

$x = 1$, $y = 3$, or $(1,3)$

Work Step by Step

Given: $y = 4 - x$ $3x + y = 6$ Subtract the first equation, $y = 4 - x$, from the second equation,$3x + y = 6$: $3x + y - (y) = 6 - (4 - x) \\3x=6-(4-x)$ Subtract each term of the binomial to obtain: $3x= 6 - 4 -(- x) \\3x=6-4+x$ Combine like terms by subtracting $x$ on both sides: $3x = 2 + x \\3x-x=2+x-x \\2x=2$ Divide both sides by $2$: $x = 1$ Substitute $x = 1$ into the first equation, $y = 4-x$: $y=4-x \\y = 4- 1 \\y=3$ Thus, $x = 1$ and $y = 3$
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