/*! 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 10 Solve each system. $$\left\\{\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 10

Solve each system. $$\left\\{\begin{array}{l} 2 x+3 y+7 z=13 \\ 3 x+2 y-5 z=-22 \\ 5 x+7 y-3 z=-28 \end{array}\right.$$

Short Answer

Expert verified
The solution of the system of equations is \(x = -204, y = 145, z = -2\).

Step by step solution

01

Eliminating a Variable

Start by eliminating one of the variables in any two of the equations. Here, choose the first and second equation and eliminate the variable x. Multiply the first equation by 3 and the second equation by 2 and then subtract the second from the first: \(6x + 9y + 21z = 39\) and \(6x + 4y - 10z = -44\). The resulting equation is \(5y + 31z = 83\). Let's call this Equation 4.
02

Further Elimination of the Same Variable

Perform the elimination step again, but this time with the first and third equation. Multiply the first equation by 5 and the third equation by 2 and then subtract the third from the first: \(10x + 15y + 35z = 65\) and \(10x + 14y - 6z = -56\). The resulting equation is \(y + 41z = 121\). Let's call this Equation 5.
03

Solve the New System of Equations from Step 1 and Step 2

From Equation 4, isolate y to get \(y = 83 - 31z\). Substituting y from Equation 4 into Equation 5 yields \(83 - 31z + 41z = 121\), simplifying gives \(z = -2\).
04

Finding y and x

Substitute \(z = -2\) into Equation 4 to find the value of y: \(y = 83 - 31*(-2) = 145\). Similarly, substitute \(z = -2\) and \(y = 145\) into the first original equation to find the value of x: \(2x + 3*145 + 7*(-2) = 13, x = -204\)

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

write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $$ \frac{5 x^{2}-9 x+19}{(x-4)\left(x^{2}+5\right)} $$

What is a system of linear equations in three variables?

Subtract: $$\frac{3}{x-4}-\frac{2}{x+2}$$

determine whether each statement makes sense or does not make sense, and explain your reasoning. I apply partial fraction decompositions for rational expressions of the form \(\frac{P(x)}{Q(x)},\) where \(P\) and \(Q\) have no common factors and the degree of \(P\) is greater than the degree of \(Q .\)

write the partial fraction decomposition of each rational expression. $$ \frac{2 x^{2}-18 x-12}{x^{3}-4 x} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.