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: 25

Answer

The solution of this system is $$x=3,\qquad y=2.$$

Work Step by Step

We will do this by following the steps below: Step 1: Subtract from the second equation the first one multiplied by $2$: $$2x-2x+y-2\times2y=8-2\times7$$ which becomes $$-3y=-6$$ and this gives $$y=2.$$ Step 2: Use the back substitution $y=2$ into the fist equation and find $x$: $$x+2\times2=7\Rightarrow x+4=7$$ and this gives $$x=3.$$
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