/*! 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 85 What is a system of linear equat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 85

What is a system of linear equations? Provide an example with your description.

Short Answer

Expert verified
A system of linear equations is a collection of two or more linear equations involving the same set of variables. A solution to a system of linear equations is a set of values that satisfy all the equations in the system simultaneously. This can be represented graphically as a point where the lines represented by each equation intersect. For example, a system of linear equations is given by \[3x+2y-1=0\] and \[2x-3y+1=0\], and its solution would be the values of \(x\) and \(y\) that satisfy both equations.

Step by step solution

01

Definition of a System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. For example, consider the following system of linear equations: \[3x+2y-1=0\] \[2x-3y+1=0\] Here, both equations are linear (degree one), and they have the same variables, x and y.
02

Describe a Solution to the System

A solution to a system of linear equations is a list of numbers that makes each equation in the system true. In other words, a solution is the set of values for the variables that satisfy all the equations in the system simultaneously. For the system given as an example, the solution would be the values of \(x\) and \(y\) that satisfy both equations.
03

Graphical Representation

Each equation in a system of linear equations can be represented graphically as a line on a two-dimensional coordinate plane. A solution to the system, as described in the previous step, is represented as the point where these lines intersect. So, if we were to graphically represent the example system, we would graph the lines represented by both equations and identify the point of intersection as the system's solution.

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

What is a constraint in a linear programming problem? How is a constraint represented?

Consider the objective function \(z=A x+B y \quad(A>0\) and \(B>0\) ) subject to the following constraints: \(2 x+3 y \leq 9, x-y \leq 2, x \geq 0,\) and \(y \geq 0 .\) Prove that the bbjective function will have the same maximum value at the vertices \((3,1)\) and \((0,3)\) if \(A=\frac{2}{3} B\)

Solve by the addition method: $$ \left\\{\begin{array}{l} 2 x+4 y=-4 \\ 3 x+5 y=-3 \end{array}\right. $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. An important application of linear programming for businesses involves maximizing profit.

Explain how to find the partial fraction decomposition of a rational expression with a prime quadratic factor in the denominator.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Statistics

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.