/*! 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 65 What is a system of linear equat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 65

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

Short Answer

Expert verified
A system of linear equations is a set of two or more linear equations that involve the same set of variables. For example: \(2x + 3y = 7\) and \(x - y = 3\) constitute a system of linear equations. The solution is the set of variable values that satisfy all equations simultaneously. For the provided example, the solution is \(x = 2\) and \(y = -1\).

Step by step solution

01

Definition

A system of linear equations is a collection of two or more linear equations that contain the same variables.
02

Example formulation

For example, the following represents a system of linear equations. \(2x + 3y = 7\) and \(x - y = 3\) . Here, \(x\) and \(y\) are the variables, the numbers \(2\), \(3\), \(7\), \(1\), and \(-1\) are coefficients, and the equals signs (\(=\)) separate the left-hand side expressions from the right-hand side expressions.
03

Solution of a system of linear equations

A solution to a system of linear equations is a set of values for the variables that satisfies all the equations simultaneously. For the given example, \(x = 2\) and \(y = -1\) are the solutions, as they satisfy both equations. You can check this by substitituting the values of \(x\) and \(y\) in both equations.

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

Without graphing, Determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}3 x+y \leq 9 \\ 3 x+y \geq 9\end{array}\right.\)

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(f(x)=x^{2}+4 x-5\)

In Exercises 41-42, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the \(x\)-variable and the \(y\)-variable is at most 4 . The \(y\)-variable added to the product of 3 and the \(x\)-variable does not exceed \(6 .\)

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & 2 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 17 \\ \hline \end{array} $$

Graph each linear inequality. \(x-y \leq 1\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

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.