/*! 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. $$\left\\{\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 6

Solve each system. $$\left\\{\begin{array}{rr} 2 x+y-2 z= & -1 \\ 3 x-3 y-z= & 5 \\ x-2 y+3 z= & 6 \end{array}\right.$$

Short Answer

Expert verified
The given system of equations has no solution due to a contradiction in our calculations.

Step by step solution

01

Simplification

The second equation can be simplified by dividing all terms by -1. This results in the following system: \[ \left\{ \begin{array}{rr} 2x + y - 2z = & -1 \ 3x + 3y + z = & -5 \ x - 2y + 3z = & 6 \end{array} \right. \]
02

Subtraction of the 1st and 2nd Equation

The 1st equation is subtracted from the 2nd, and this provides a new 2nd equation. This results in the system: \[ \left\{ \begin{array}{rr} 2x + y - 2z = & -1 \ x - 2z = & -4 \ x - 2y + 3z = & 6 \end{array} \right. \]
03

Solve for \(x\)

By solving the modified 2nd equation, we obtain \(x = 4\).
04

Substitute \(x\)

Substitute \(x = 4\) in the 1st and 3rd equation and solve for \(y\): \[ \left\{ \begin{array}{rr} y = & 2 \ y = & 3 \end{array} \right. \] This is a contradiction as \(y\) can't be 2 and 3 at the same time.
05

Conclusion

This system of equations has no solution as we have a contradiction in Step 4 with respect to the value of \(y\).

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

At a college production of \(A\) Streetcar Named Desire, 400 tickets were sold. The ticket prices were 8 dollar ,10 dollar, and 12 dollar, and the total income from ticket sales was 3700 dollar. How many tickets of each type were sold if the combined number of 8 dollar and 10 dollar tickets sold was 7 times the number of 12 dollar tickets sold?

write the partial fraction decomposition of each rational expression. $$ \frac{1}{x^{2}-c^{2}} \quad(c \neq 0) $$

will help you prepare for the material covered in the next section. Graph \(x-y=3\) and \((x-2)^{2}+(y+3)^{2}=4\) in the same rectangular coordinate system. What are the two intersection points? Show that each of these ordered pairs satisfies both equations.

Solve the system: $$\left\\{\begin{aligned} x+y+2 z &=19 \\ y+2 z &=13 \\ z &=5 \end{aligned}\right.$$ What makes it fairly easy to find the solution?

How can you verify your result for the partial fraction decomposition for a given rational expression without using a graphing utility?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.