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Solve the system $x+y=4, y+z=-3,$ and $x+z=-17$.

   Solve the system $x+y=4, y+z=-3,$ and $x+z=-17$.

Precalculus Functions and Graphs

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 9, Problem 77

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Solved by Expert Xiaomeng Zhang

04/14/2020

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Solve the system $x+y=4, y+z=-3,$ and $x+z=-17$.

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Key Concepts

Elimination Method

The elimination method is a technique used to solve systems of linear equations by removing one variable at a time, which simplifies the system to a smaller set of equations. This is done by adding or subtracting equations after multiplying them by appropriate constants, allowing one to isolate and solve for individual variables. This method is particularly useful when the system is structured in a way that makes direct substitution cumbersome or when quick cancelation of terms is possible.

Systems of Linear Equations

A system of linear equations consists of multiple equations that share common variables, and the goal is to find values for these variables that satisfy all the equations simultaneously. This concept is fundamental in algebra and is applicable to various areas of mathematics and applied sciences. Solving such systems can involve methods like substitution, elimination, or using matrix techniques, and understanding the structure of these systems is crucial for both theoretical and practical problem-solving.

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