Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions
7. $|x + 2 y + 3 z = 1 x + 3 y + 4 z = 3 x + 4 y + 5 z = 4|$

The system of equation has no solution.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:Transforming the system

To get the solution, we will transform the value ofx,y,z.

$|x + 2 y + 3 z = 1 . . . . . . (1) x + 3 y + 4 z = 3 . . . . . . (2) x + 4 y + 5 z = 4 . . . . . . (3)|$ Into the form $|x = . . . . y = . . . . z = . . .|$

Step 2: Eliminating the variables

In the given system of equations, we can eliminate the variables by adding or subtracting the equations.

In this system, we can eliminate the variable x from equation 2 and 3. First of all subtract the equation 1 from equation 2 and then subtract the first equation from equation 3.

$\begin{array}{rcl} |x + 2 y + 3 z = 1 x - x + 3 y - 2 y + 4 z - 3 z = 3 - 1 x - x + 4 y - 2 y + 5 z - 3 z = 4 - 1| & = & |x + 2 y + 3 z = 1 y + z = 2 2 y + 2 z = 3| \end{array}$

Now multiply equation 2 by 2 and then subtract equation 2 from equation 3.

$\begin{array}{rcl} |x + 2 y + 3 z = 1 2 y + 2 z = 4 2 y + 2 z = 3| & = & |x + 2 y + 3 z = 1 0 = 1 2 y + 2 z = 3| \end{array}$

For whatever the value of the value 0 will never equal to 1. Thus, the given system of equations is inconsistent.

Hence, the given system of the equation has no solution.

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Linear Algebra With Applications

Answers without the blur.

Short Answer

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions
7. $|x + 2 y + 3 z = 1 x + 3 y + 4 z = 3 x + 4 y + 5 z = 4|$

Step by Step Solution

Step 1:Transforming the system

Step 2: Eliminating the variables

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Linear Algebra With Applications

Answers without the blur.

Short Answer

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions7. x+2y+3z=1x+3y+4z=3x+4y+5z=4

Step by Step Solution

Step 1:Transforming the system

Step 2: Eliminating the variables

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

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In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions
7. $|x + 2 y + 3 z = 1 x + 3 y + 4 z = 3 x + 4 y + 5 z = 4|$