Elementary Technical Mathematics

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

Chapter 9 - Section 9.1 - Solving Pairs of Linear Equations by Graphing - Exercises - Page 327: 13

Answer

($-\frac{14}{3}$,$-\frac{13}{3}$) or $(-4.67,-4.33)$

Work Step by Step

To solve this system of equations, we use the graphing method $5x+8y=-58$ $2x+2y=-18$ Taking the first equation, we solve for $y$. $5x+8y=-58$ $8y=-58-5x$ $y=\frac{-58-5x}{8}$ Find three solutions: For x=2, $y=\frac{-58-5x}{8}$ $y=\frac{-58-5(2)}{8}$ $y=-8.5$ For x=0, $y=\frac{-58-5x}{8}$ $y=\frac{-58-5(0)}{8}$ $y=-7.25$ For x=-2, $y=\frac{-58-5x}{8}$ $y=\frac{-58-5(-2)}{8}$ $y=-6$ With the three points, $(2,-8.5), (0,-7.25), (-2,-6)$ we can graph the straight line that goes through these points. Taking the second equation, we solve for $y$. $2x+2y=-18$ $2y=-18-2x$ $y=\frac{-18-2x}{2}$ Find three solutions: For x=2, $y=\frac{-18-2x}{2}$ $y=\frac{-18-2(2)}{2}$ $y=-11$ For x=0, $y=\frac{-18-2x}{2}$ $y=\frac{-18-2(0)}{2}$ $y=-9$ For x=-2, $y=\frac{-18-2x}{2}$ $y=\frac{-18-2(-2)}{2}$ $y=-7$ With the three points, $(2,-11), (0,-9), (-2,-7)$ we can graph the straight line that goes through these points. The intersection point between these two lines is the answer to the system of equations.
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