Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 9 - Section 9.2 - Solving Pairs of Linear Equations by Addition - Exercises - Page 332: 41


One common solution $\Rightarrow$ $(\frac{1}{4},\frac{2}{5})$

Work Step by Step

We use the addition method below: We add the two equations: $16x+5y=6$ $7x+\frac{5}{8}y=2$ Multiply the first equation by $7$ and the second equation by $-16$ to cancel $x$: $+112x+35y=+42$ $\underline{-112x-10y=-32}$ $25y=10$ Solve for $y$: $y=\frac{10}{25}=\frac{2}{5}$ Substitute into any of the two equations and solve for $x$: $16x+5(\frac{2}{5})=6$ $16x+2=6$ $16x=6-2$ $16x=4$ $x=\frac{4}{16}$ Reduce the fraction: $x=\frac{1}{4}$
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