/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 What is a system of linear equat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 47

What is a system of linear equations in three variables?

Short Answer

Expert verified
A system of linear equations in three variables is a set of two or more linear equations that all contain the same three variables. The equations need to be solved together to find the variable values that satisfy all equations.

Step by step solution

01

Definition

A system of linear equations in three variables is a set of two or more linear equations that all contain the same three variables. The equations are interconnected, meaning that the solution to the system, if one exists, must satisfy all the equations simultaneously.
02

Form of the equations

The standard form of each linear equation in the system is \(Ax + By + Cz = D\), where A, B, C, and D are constants and x, y, and z are the variables. A, B, and C are the coefficients of the variables, and D is the constant term.
03

Types of Solutions

The system of equations can have one unique solution, infinitely many solutions, or no solution at all. If the system does have a solution, it corresponds to the point of intersection of the planes represented by the equations in a three-dimensional space.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When I use the addition method, I sometimes need to multiply more than one equation by a nonzero number before adding the equations.

The manager of a candystand at a large multiplex cinema has a popular candy that sells for \(\$ 1.60\) per pound. The manager notices a different candy worth \(\$ 2.10\) per pound that is not selling well. The manager decides to form a mixture of both types of candy to help clear the inventory of the more expensive type. How many pounds of each kind of candy should be used to create a 75 -pound mixture selling for \(\$ 1.90\) per pound?

Write the slope-intercept form of the equation of the line passing through \((-5,6)\) and \((3,-10)\)

Graph each equation. \(y=-5\) (Section 3.2, Example 7)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.