Question

Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. See the procedure for the Gaussian elimination method for two equations on page 627. $\begin{aligned} x+y &=5 \\-2 x+y &=-1 \end{aligned}$

Name: Problem 35, Chapter 9: Precalculus Functions and Graphs
Uploaded: 2020-04-10T20:36:42-08:00
Duration: 2 min 5 s
Channel: Xiaomeng Zhang
Description: Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. See the procedure for the Gaussian elimination method for two equations on page 627. x+y =5 -2 x+y =-1

   Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. See the procedure for the Gaussian elimination method for two equations on page 627.

$\begin{aligned} x+y &=5 \\-2 x+y &=-1 \end{aligned}$

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 9, Problem 35

Instant Answer

Solved by Expert Xiaomeng Zhang

04/10/2020

Step 1

Step 1: First, we write the system of equations in augmented matrix form: $\begin{bmatrix} 1 & 1 & 5 \\ -2 & 1 & -1 \end{bmatrix}$ Show more…

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Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. See the procedure for the Gaussian elimination method for two equations on page 627. $\begin{aligned} x+y &=5 \\-2 x+y &=-1 \end{aligned}$

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Key Concepts

System Classification

Systems of equations are classified as independent, dependent, or inconsistent. An independent system has a unique solution, a dependent system has infinitely many solutions because one equation can be derived from another, and an inconsistent system has no solution due to conflicting constraints among the equations.

Gaussian Elimination

Gaussian elimination is a method utilized to solve systems of linear equations by systematically applying row operations to convert the system into an upper triangular or row-echelon form, from which back-substitution can be easily performed.

Systems of Linear Equations

Systems of linear equations consist of multiple linear equations involving the same set of variables, and the goal is to determine the values of these variables that satisfy all the equations simultaneously.

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