/*! 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 89 When is it easier to use the add... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 89

When is it easier to use the addition method rather than the substitution method to solve a system of equations?

Short Answer

Expert verified
The addition method is typically easier to use than the substitution method when the equations are arranged such that the coefficients of one variable are the same in both equations or negatives of each other. This allows for straightforward elimination of that variable. However, overall the choice between methods really depends on the specific system of equations that is given. In cases where one variable is easily isolated in one of the equations, the substitution method may be simpler.

Step by step solution

01

Understand the Addition Method

The addition method, also known as the elimination method, involves adding or subtracting the equations in order to eliminate one of the variables. This method is quite straightforward when the coefficients of one of the variables are the same in both equations, because simply adding or subtracting the equations will eliminate that variable. For instance, consider two equations: equation 1, \(2x + 3y = 12\) and equation 2, \(2x - y = 2\). Adding these two equations results in \(4x + 2y = 14\), and \(y\) can be easily isolated to solve for \(x\).
02

Understand the Substitution Method

The substitution method involves isolating one variable in one equation and then substituting that expression into the other equation. This method is typically easier when one of the variables in one of the equations is already isolated, or can be isolated with just one operation. For example, given the equation 1: \(y = 3x -1\) and equation 2: \(2x + y = 4\), \(y\) is already isolated in equation 1, so it is easier to substitute \(3x -1\) into equation 2 for \(y\).
03

Compare the Methods

Looking at both methods, it can be concluded that the addition (elimination) method can be significantly easier to use than the substitution method when the coefficients of one of the variables in the equations are the same or negatives of each other. Otherwise, if the coefficients are not easily manageable or one of the variables cannot be easily eliminated, it may be simpler to use the substitution method, particularly when one of the variables in one of the equations is already isolated or can be isolated with one operation.

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

determine whether each statement makes sense or does not make sense, and explain your reasoning. Use an extension of the Great Question! on page 859 to describe how to set up the partial fraction decomposition of a rational expression that contains powers of a prime cubic factor in the denominator. Give an example of such a decomposition.

Consider the following equations: \(\left\\{\begin{array}{l}{5 x-2 y-4 z=3} \\ {3 x+3 y+2 z=-3}\end{array}\right.\) Eliminate \(z\) by copying Equation \(1,\) multiplying Equation 2 by \(2,\) and then adding the equations.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed the solution set of \(y\) as \(x+2\) and \(x \geq 1\) without using test points.

Exercises \(41-43\) will help you prepare for the material covered in the first section of the next chapter. Solve the system: $$ \left\\{\begin{aligned} x+y+2 z &=19 \\ y+2 z &=13 \\ z &=5 \end{aligned}\right. $$

When a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let \(x=\) the crew's rowing rate in still water and let \(y=\) the rate of the current. The following chart summarizes this information:
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.