/*! 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 6 Solve each system by graphing. C... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 6

Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}x+y=2 \\ x-y=4\end{array}\right.\)

Short Answer

Expert verified
The solution to the system of equations is the intersection point of the two lines when graphed. Verification is done by substituting the coordinates of this point into the original equations.

Step by step solution

01

Rearrange the Equations in Slope-Intercept Form

The slope-intercept form of the equation of a line is given as y = mx + c, where m is the slope of the line and c is the y-intercept. Rearrange the equations as follows:For the first equation: \( x+y=2 \) ----> \( y = -x + 2 \)For the second equation: \( x-y=4 \) ----> \( y = x - 4 \)
02

Graph the Equations

Graph the two lines defined by the equations \( y=-x+2 \) and \( y=x-4 \). When these two lines are plotted, their intersection point is the solution of the system of equations.
03

Find the Intersection Point

By observing or plotting the graph, the intersection point of the two lines can be found. This point (x,y) is where both equations are satisfied simultaneously.
04

Check the Solution

Finally, validate this solution by substituting the x and y coordinates of the intersection point into both of the original equations to confirm that they hold true.

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

Graph each linear inequality. \(x \leq-4\)

Graph each linear inequality. \(y>-4\)

Graph each linear inequality. \(3 x+y \leq 3\)

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12\), it's not necessary for me to graph the linear equation \(3 x-4 y=12\) because the inequality contains a \(<\) symbol, in which equality is not included.

A patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol. Each ounce of meat provides 110 milligrams. a. Write an inequality that describes the patient's dietary restrictions for \(x\) eggs and \(y\) ounces of meat. b. Graph the inequality. Because \(x\) and \(y\) must be positive, limit the graph to quadrant I only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.