Q. 368 Determine whether the ordered tr... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q. 368 (page 481)

Determine whether the ordered triple is a solution to the system.
$\{\begin{cases} 3 x - 4 y - 3 z = 2 \\ 2 x - 6 y + z = 3 \\ 2 x + 3 y - 2 z = 3 \end{cases}$
(a) $(2, 3, - 1)$
(b) $(3, 1, 3)$

Short Answer

Expert verified

(a) The ordered triple $(2, 3, - 1)$ is not a solution to the system of linear equations.

(b) The ordered triple $(3, 1, 3)$ is not a solution of the system of linear equations.

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} 3 x - 4 y - 3 z = 2 . . . . . . . . . . (1) \\ 2 x - 6 y + z = 3 . . . . . . . . . . . (2) \\ 2 x + 3 y - 2 z = 3 . . . . . . . . . (3) \end{cases}$

Part a Step 1. Finding whether (2,3,-1) satisfies equation (1)

Substituting $x = 2 y = 3 z = - 1$ in the equation

$3 x - 4 y - 3 z = 2$ ,

$3 (2) - 4 (3) - 3 (1) = 2 6 - 12 - 3 = 2 6 - 15 = 2 - 9 鈮� 2$

Part a. Step 2. Finding whether (2,3,-1) satisfies equation (2).

Substituting $x = 2 y = 3 z = - 1$ in the equation

$2 x - 6 y + z = 3$ ,

$2 (2) - 6 (3) + (- 1) = 3 4 - 18 - 1 = 3 4 - 19 = 3 - 15 鈮� 3$

Part a. Step 3. Finding whether (2,3,-1) is a solution of equation (3).

Substituting $x = 2 y = 3 z = - 1$ in the equation

$2 x + 3 y - 2 z = 3$ ,

$2 (2) + 3 (3) - 2 (- 1) = 3 4 + 9 + 2 = 3 15 鈮� 3$

The ordered triple $(2, 3, - 1)$ is not a solution to the system of linear equations.

Part b. Step 1. Finding whether (3,1,3) is a solution of equation (1).

Substituting $x = 3 y = 1 z = 3$ in the equation

$3 x - 4 y - 3 z = 2$ ,

$3 (3) - 4 (1) - 3 (3) = 2 9 - 4 - 9 = 2 - 4 鈮� 2$

Part b. Step 2. Finding whether (3,1,3) is a solution to equation (2).

Substituting $x = 3 y = 1 z = 3$ in the equation

$2 x - 6 y + z = 3$ ,

$2 (3) - 6 (1) + 3 = 3 6 - 6 + 3 = 3 3 = 3$

Part b. Step 3. Finding whether (3,1,3) is a solution for equation (3).

Substituting $x = 3 y = 1 z = 3$ in the equation

$2 x + 3 y - 2 z = 3$ ,

$2 (3) + 3 (1) - 2 (3) = 3 6 + 3 - 6 = 3 3 = 3$

The ordered triple $(3, 1, 3)$ is not a solution for the system of equations

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Determine whether the ordered triple is a solution to the system.
$\{\begin{cases} 3 x - 4 y - 3 z = 2 \\ 2 x - 6 y + z = 3 \\ 2 x + 3 y - 2 z = 3 \end{cases}$
(a) $(2, 3, - 1)$
(b) $(3, 1, 3)$

Short Answer

Step by step solution

Step 1. Given the information

Part a Step 1. Finding whether (2,3,-1) satisfies equation (1)

Part a. Step 2. Finding whether (2,3,-1) satisfies equation (2).

Part a. Step 3. Finding whether (2,3,-1) is a solution of equation (3).

Part b. Step 1. Finding whether (3,1,3) is a solution of equation (1).

Part b. Step 2. Finding whether (3,1,3) is a solution to equation (2).

Part b. Step 3. Finding whether (3,1,3) is a solution for equation (3).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Probability and Statistics

Logic and Functions

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Determine whether the ordered triple is a solution to the system.3x-4y-3z=22x-6y+z=32x+3y-2z=3(a) (2,3,-1)(b)(3,1,3)

Short Answer

Step by step solution

Step 1. Given the information

Part a Step 1. Finding whether (2,3,-1) satisfies equation (1)

Part a. Step 2. Finding whether (2,3,-1) satisfies equation (2).

Part a. Step 3. Finding whether (2,3,-1) is a solution of equation (3).

Part b. Step 1. Finding whether (3,1,3) is a solution of equation (1).

Part b. Step 2. Finding whether (3,1,3) is a solution to equation (2).

Part b. Step 3. Finding whether (3,1,3) is a solution for equation (3).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Probability and Statistics

Logic and Functions

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Determine whether the ordered triple is a solution to the system.
$\{\begin{cases} 3 x - 4 y - 3 z = 2 \\ 2 x - 6 y + z = 3 \\ 2 x + 3 y - 2 z = 3 \end{cases}$
(a) $(2, 3, - 1)$
(b) $(3, 1, 3)$