/*! 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 45 When using the substitution meth... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 45

When using the substitution method, how can you tell if a system of linear equations has no solution?

Short Answer

Expert verified
A system of linear equations has no solution using the substitution method when the substitution leads to an impossible or untrue statement, such as 0 equals a non-zero number.

Step by step solution

01

Understand the Substitution Method

In the substitution method, the goal is to express one variable from one equation in terms of the other variable(s), and then substitute this expression into the other equation(s). As a result, one should get an equation which involves only one variable and can be solved directly.
02

Apply the Substitution

Substitute the expression obtained in step one into the other equation(s). This should provide an equation involving only one variable, which can then be solved.
03

Determine the Absence of Solution

In cases where the equations have no solution, you would obtain a contradiction during the substitution process. For instance, you might obtain a statement like \(0=3\), which is clearly untrue.
04

Example

Consider two equations, \(x+2y=3\) and \(2x+4y=7\). Here, substituting \(x = 3 - 2y\) into the second equation results in \(2(3-2y) + 4y = 7\), which simplifies to \(6-4y +4y=7\) or \(6=7\), a contradiction, thus indicating that the system has no 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

When using the addition method, how can you tell if a system of linear equations has no solution?

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. Each equation in a system of linear equations has infinite many ordered-pair solutions.

Simplify: \(5+6(x+1)\)

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. $$\left\\{\begin{array}{l} x+y=11 \\ \frac{x}{5}+\frac{y}{7}=1 \end{array}\right.$$

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

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Pure 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.