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3.10x+7y-2z=46 3x-2y+9z%3D22 5x+y-3z%3D28

3.10x+7y-2z=46 3x-2y+9z%3D22 5x+y-3z%3D28

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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solve each system of equations. 

**System of Linear Equations** Consider the following system of linear equations that needs to be solved: 1. \( 10x + 7y - 2z = 46 \) 2. \( 3x - 2y + 9z = 22 \) 3. \( 5x + y - 3z = 28 \) **Explanation:** - The given system represents three linear equations with three variables: \( x \), \( y \), and \( z \). - The goal is to find the values of \( x \), \( y \), and \( z \) that satisfy all three equations simultaneously. **Steps to Solve the System:** 1. **Identify the coefficients and constants:** - For equation 1: coefficients are \(10\) for \(x\), \(7\) for \(y\), \(-2\) for \(z\), and the constant term is \(46\). - For equation 2: coefficients are \(3\) for \(x\), \(-2\) for \(y\), \(9\) for \(z\), and the constant term is \(22\). - For equation 3: coefficients are \(5\) for \(x\), \(1\) for \(y\), \(-3\) for \(z\), and the constant term is \(28\). 2. **Choose a method to solve the system:** - You can use substitution, elimination, or matrix methods (Gaussian elimination or Cramer’s rule) to find the values of \( x \), \( y \), and \( z \). **Recommended Exercises:** - Try solving this system using the elimination method. - Use matrix operations to solve the system if you are familiar with linear algebra concepts. This exercise will help reinforce your understanding of solving systems of linear equations and applying different methods to find solutions.
Transcribed Image Text:**System of Linear Equations** Consider the following system of linear equations that needs to be solved: 1. \( 10x + 7y - 2z = 46 \) 2. \( 3x - 2y + 9z = 22 \) 3. \( 5x + y - 3z = 28 \) **Explanation:** - The given system represents three linear equations with three variables: \( x \), \( y \), and \( z \). - The goal is to find the values of \( x \), \( y \), and \( z \) that satisfy all three equations simultaneously. **Steps to Solve the System:** 1. **Identify the coefficients and constants:** - For equation 1: coefficients are \(10\) for \(x\), \(7\) for \(y\), \(-2\) for \(z\), and the constant term is \(46\). - For equation 2: coefficients are \(3\) for \(x\), \(-2\) for \(y\), \(9\) for \(z\), and the constant term is \(22\). - For equation 3: coefficients are \(5\) for \(x\), \(1\) for \(y\), \(-3\) for \(z\), and the constant term is \(28\). 2. **Choose a method to solve the system:** - You can use substitution, elimination, or matrix methods (Gaussian elimination or Cramer’s rule) to find the values of \( x \), \( y \), and \( z \). **Recommended Exercises:** - Try solving this system using the elimination method. - Use matrix operations to solve the system if you are familiar with linear algebra concepts. This exercise will help reinforce your understanding of solving systems of linear equations and applying different methods to find solutions.
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