/*! 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 43 Describe the conditions in a pro... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 43

Describe the conditions in a problem that enable it to be solved using a system of linear equations.

Short Answer

Expert verified
A problem can be solved using a system of linear equations if it involves finding the values of variables that satisfy two or more equations simultaneously, each of the equations represents a straight-line relationship with a constant rate of change, and the solution requires finding the points where these lines intersect.

Step by step solution

01

Definition of a linear equation

A linear equation in two variables is an equation that can be expressed in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants, and \(x\) and \(y\) are variables. A system of linear equations is a collection of two or more linear equations involving the same set of variables.
02

Identify Problems Suitable for System of Linear Equations

There are certain conditions under which a problem can be solved using a system of linear equations. These conditions include: 1) The problem involves finding the values of variables that satisfy more than one equation simultaneously. 2) Each equation represents a straight-line relationship between two variables or more, and there is a constant rate of change. 3) The problem solution requires finding the point(s) where these lines intersect, representing the solution to all equations in the system.
03

Application of a system of linear equations

Systems of linear equations are incredibly versatile and are applied across a vast range of fields. They are used to model and solve real-world problems in physics, engineering, business, and economics. Examples of problems suited to this approach might include finding the optimal combination of resources to minimize cost or maximize profit, planning and scheduling for optimum efficiency, or analyzing data trends.

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

Verify your solutions to any five exercises from Exercises 11 through 36 by using a graphing utility to graph the two equations in the system in the same viewing rectangle. After entering the two equations, one as \(y_{1}\) and the other as \(y_{2},\) and graphing them, use the \([\text { INTERSECTION }]\) feature to find the system's solution. (It may first be necessary to solve the equations for \(y\) before entering them.)

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}x+2 y=4 \\ x-y=4\end{array}\right.$$

Tourist: "How many birds and lions do you have in your zoo?" Zookeeper: "There are 30 heads and 100 feet." Tourist: "I can't tell from that." Zookeeper: "Oh, yes, you can!" Can you? Find the number of each.

One apartment is directly above a second apartment. The resident living downstairs calls his neighbor living above him and states, "If one of you is willing to come downstairs, we'll have the same number of people in both apartments." The upstairs resident responds, "We're all too tired to move. Why don't one of you come up here? Then we'll have twice as many people up here as you've got down there." How many people are in each apartment?

Will help you prepare for the material covered in the next section. In each exercise, solve the given equation. $$(5 x-1)+1=5 x+5$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.