/*! 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 93 When solving a system of equatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 93

When solving a system of equations by substitution, how do you recognize that the system has no solution?

Short Answer

Expert verified
If, while applying the substitution method to a system of equations, one derives a false statement, the system is deemed to have no solution. This scenario represents parallel lines that do not intersect.

Step by step solution

01

Step 1- Understand the concept of No Solution

In a system of equations, 'no solution' means that the lines do not intersect, and therefore there is no x, y (or z) that satisfies both equations at the same time. When the systems of equations have the same slope and different y-intercepts, they are parallel and never cross each other. Hence, there will be no solution for such systems.
02

- Implementation of substitution method

Begin by solving one of the equations for either of the variables. Substitute the expression obtained into the other equation of the system. The result is an equation in one variable.
03

Step 3- Carrying out necessary operations

Solve the single-variable equation. If at this point the result is a true mathematical statement such as 4=4, it confirms the system of equations has an infinite number of solutions. If the resulting statement is false, such as 5=0, this means the system of equations 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

Find the general form of the equation of the line that passes through the two points. \((-4,12),(4,2)\)

(A) find the determinant of \(A,\) (b) find \(A^{-1},\) (c) find \(\operatorname{det}\left(A^{-1}\right),\) and (d) compare your results from parts (a) and (c). Make a conjecture based on your results. $$A=\left[\begin{array}{rrr} -1 & 3 & 2 \\ 1 & 3 & -1 \\ 1 & 1 & -2 \end{array}\right]$$

Write the matrix in row-echelon form. Remember that the row-echelon form of a matrix is not unique. $$\left[\begin{array}{rrrr} 1 & -3 & 0 & -7 \\ -3 & 10 & 1 & 23 \\ 4 & -10 & 2 & -24 \end{array}\right]$$

Determine whether the statement is true or false. Justify your answer. If a system of linear equations has two distinct solutions, then it has an infinite number of solutions.

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to find the solution. (Use the variables \(x, y,\) and \(z,\) if applicable.) $$\left[\begin{array}{rrrrr} 1 & -1 & 4 & \vdots & 0 \\ 0 & 1 & -1 & \vdots & 2 \\ 0 & 0 & 1 & \vdots & -2 \end{array}\right]$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.