Chapter 11: Q. 79 (page 757)

In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 5 x - y + 4 z = 2 \\ - x + 5 y - 4 z = 3 \\ 7 x + 13 y - 4 z = 17 \end{cases}$

Short Answer

Expert verified

The given equation $\{\begin{cases} 5 x - y + 4 z = 2 \\ - x + 5 y - 4 z = 3 \\ 7 x + 13 y - 4 z = 17 \end{cases}$ has no solution.Hence the system is incosistent

Step by step solution

Step 1. Given inforrmation

The given equations $\{\begin{cases} 5 x - y + 4 z = 2 \\ - x + 5 y - 4 z = 3 \\ 7 x + 13 y - 4 z = 17 \end{cases}$

Step 2. Finding the values of x,y and z

Consider the equations $5 x - y + 4 z = 2, - x + 5 y - 4 z = 3$ and $7 x + 13 y - 4 z = 17$ .To solve these equations,it seems easiest to eliminate the variable first.So,we add the first two equations

localid="1647429180260" $5 x - y + 4 z = 2 + - x + 5 y - 4 z = 3 4 x + 4 y + 0 z = 5$

$4 x + 4 y + 0 z = 5 \dots \dots (1)$

Now,we substract the last equation from the second equation

$- - x + 5 y - 4 z = 3 7 x + 13 y - 4 z = 17 - 8 x - 8 y + 0 z = - 14$

$- 8 x - 8 y + 0 z = - 14 \dots \dots (2)$

We multiplay equation (1) by 2 and equation (2)

$8 x + 8 z = 10 - 8 x - 8 y = 14 0 x + 0 y = - 4$

$0 x + 0 y = - 4 \dots \dots (3)$

Equation (3) has no solution.Hence the system is incosistent

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 5 x - y + 4 z = 2 \\ - x + 5 y - 4 z = 3 \\ 7 x + 13 y - 4 z = 17 \end{cases}$

Short Answer

Step by step solution

Step 1. Given inforrmation

Step 2. Finding the values of x,y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 75– 82, algebraically solve each system of equations using any method you wish.5x-y+4z=2-x+5y-4z=37x+13y-4z=17

Short Answer

Step by step solution

Step 1. Given inforrmation

Step 2. Finding the values of x,y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 75– 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 5 x - y + 4 z = 2 \\ - x + 5 y - 4 z = 3 \\ 7 x + 13 y - 4 z = 17 \end{cases}$