Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 22: 28


The solution of this system is $$x=\frac{1}{5}\qquad y= \frac{1}{2}.$$

Work Step by Step

Follow the steps bellow: Step 1: Subtract from the second equation the first one multiplied by $3/2$ to eliminate $x$: $$3x-\frac{3}{2}2x+2y-\frac{3}{2}(-y) =1.6-\frac{3}{2}(-0.1)\Rightarrow 3x-3x+2y+\frac{3}{2}y = 1.6+0.15$$ which becomes $$\frac{7}{2}y = 1.75 = \frac{7}{4}$$ and this gives $$y=\frac{1}{2}.$$ Step 2: Use back substitution to find $x$ from the 1st equation: $$2x-\frac{1}{2} = -0.1\Rightarrow 2x=\frac{1}{2}-0.1\Rightarrow 2x = 0.5-0.1 = 0.4=\frac{2}{5}.$$ this gives $$x=\frac{1}{5}.$$
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