**Solving a System of Equations**To solve the following system of linear equations:1. \( 4x - 3y - 2z = 21 \)2. \( 6y - 5z = -8 \)3. \( z = -2 \)We will follow the step-by-step process:First, substitute the value of \( z \) from the third equation into the first and second equations:Substituting \( z = -2 \) in:1. \( 4x - 3y - 2(-2) = 21 \)2. \( 6y - 5(-2) = -8 \)This simplifies to:1. \( 4x - 3y + 4 = 21 \) 2. \( 6y + 10 = -8 \)Next, simplify these new equations:1. \( 4x - 3y + 4 = 21 \) becomes \( 4x - 3y = 17 \)2. \( 6y + 10 = -8 \) becomes \( 6y = -18 \), and then further simplifies to \( y = -3 \)Now substitute \( y = -3 \) back into the simplified first equation:1. \( 4x - 3(-3) = 17 \) simplifies to \( 4x + 9 = 17 \)Subtract 9 from both sides:1. \( 4x = 8 \)Then, divide both sides by 4:1. \( x = 2 \)Thus, we have \( x = 2 \), \( y = -3 \), and \( z = -2 \).The correct solution is:\[ (2, -3, -2) \]The available options are:- \( \emptyset \) (the null set)- \( (2, -3, -2) \)- \( (8, 4, -2) \)**Conclusion:**The correct answer is \((2, -3, -2)\).Note on the interface: The image also includes a back arrow on the left side, typically used for navigation purposes in digital content, and a system notification at the bottom, showing a scheduled event (STL - NYM in 3 hours). These elements do not affect the problem-solving process.

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Answered: Solve the following system of…

Solve the following system of equations: (1) 4x-3y-2z= 21 (2) 6y- 5z = -8 (3) Z = -2 O Ø (the null set) O (2, -3, -2) O (8,4,-2)

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter5: Systems Of Linear Equations

Section5.4: Solve Applications With Systems Of Equations

Problem 5.85TI: Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles...

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