/*! 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 57 Explain how to solve a system of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 57

Explain how to solve a system of linear equations by graphing.

Short Answer

Expert verified
The system of linear equations is solved by graphing the individual equations and identifying their point, or points, of intersection, which is the solution to the system.

Step by step solution

01

Understand the Equations

First, take a quick look at your linear equations. Make sure they're in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. If they're not in this form, rearrange them. These equations will create straight lines when graphed.
02

Graph the Equations

The next step is to draw each equation on a graph. Plot the y-intercept first, then use the slope to find a second point for each line. Sketch the lines extending through these points.
03

Identify Intersection

Look at the graph and identify where the lines intersect each other. That point represents the x and y values that solve the system of equations.
04

Write the Solution

The solution of a system of equations represented by graph is the point of intersection. Identify the x and y coordinates of the point, and write them as an ordered pair \((x, y)\). This is the solution to the system.

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

Exercises \(89-91\) will help you prepare for the material covered in the next section. The sum of two numbers, \(x\) and \(y,\) is \(28 .\) The difference between the numbers is 6 a. Write a system of linear equations that models these conditions. b. Solve the system and find the numbers.

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} \frac{x}{3}+y=3 \\ \frac{x}{2}-\frac{y}{4}=1 \end{array}\right.$$

In Exercises \(57-60\), write a system of equations modeling the given conditions. Then solve the system by the addition method and find the two numbers. Three times a first number increased by twice a second number is \(11 .\) The difference between the first number and twice the second number is 9. Find the numbers.

In Exercises \(61-68,\) solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{array}{l} \frac{x}{2}=\frac{y+8}{4} \\ \frac{x+3}{2}=\frac{y+5}{4} \end{array}\right.$$

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}y=2 x+2 \\ y=-2 x+6\end{array}\right.$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics 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.