Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 8 - Systems of Linear Equations and Problem Solving - Connecting: The Concepts - Exercises - Page 516: 3



Work Step by Step

Equation 1 has variables isolated - select the substitution method. $y=\displaystyle \frac{1}{2}x+1\qquad $(*) Replace y with $\displaystyle \frac{1}{2}x+1$ in the second equation: $\displaystyle \frac{1}{2}x+1=2\mathrm{x}-5\qquad$ ... and solve for $x$. Multiply with 2 $ x+2=4x-10\qquad$ ... add $10-x$ to both sides $ 12=3x\qquad$ ... divide with 3 $4=x$ Now, back-substitute into (*) $y=\displaystyle \frac{1}{2}(4)+1=2+1=3$ Form an ordered pair $(x,y) $ as the solution to the system $(4,3)$
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