Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.1 Systems of Linear Equations: Substitution and Elimination - 10.1 Assess Your Understanding - Page 735: 47

Answer

$\{(x,y,z)|x=5z-2, y=4z-3\}$

Work Step by Step

1. Add the 2nd and the 3rd equations to get $2x-10z=-4$ or $x-5z=-2$ 2. Multiply 2 to the 1st equation, then add to the 2nd to get $x-5z=-2$ 3. As the two equations above are identical, the system is dependent. 4. We have $x=5z-2$ and from the 1st eqn, we have $y=x-z-1=4z-3$ 5. Solution $\{(x,y,z)|x=5z-2, y=4z-3\}$ where $z$ is any real number.
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