EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 7.3, Problem 41E

To determine

The solution of the given equation x−2y+5z=2; 4x −z=0

Expert Solution & Answer

Answer to Problem 41E

(2a, 21a−1, 8a) is the solution of the given equation.

Explanation of Solution

Given:

The given system of equation is

x−2y+5z=24x −z=0

Formula used:

Gaussian elimination and back substitution method is used.

Calculation:

Let’s consider the following system,

x−2y+5z=24x −z=0

By using the Gaussian elimination method to solve the system. The given system has two equations and three variables. Therefore, the system does not have a unique solution.

Now, by rewriting the system it row - echelon form.

Multiply the first equation by -4.

−4(x−2y+5z=2)−4x+8y−20z=−8

Now, adding the obtained equation and the second equation of the system.

−4x+8y−20z=−84x −z=0−−−−−−−−−−− 8y−21z=−8

Therefore, the new system is

x−2y+5z=2 8y−21z=−8

Multiply the second equation by 18

18(8y−21z=−8)y−218z=−1

Therefore, the new system in row - echelon form is

x−2y+5z=2 y−218z=−1

Now solving y in terms of z.

y−218z=−1 y=−1+218z

Back substituting y=−1+218z in the first equation, solve for x.

Therefore,

x−2y+5z=2x−2(−1+218z)+5z=2 x+2−214z+5z=2 x=2−2+214z−5z x=14z

Let us assume that z=8a , where is a real number, the solution is obtained as follows,.

x=14(8a)x=2a

y=−1+218(8a)y=−21a+1

and

z=8a

Therefore, the solution of the given system of equations is (2a, 21a−1, 8a) , where a is a real number.

To check that (2a, 21 a−1, 8a) is the solution of the given system, substituting x=2a, y=21a+1 and z=8a i1 both the equations of the system and see whether the equations are satisfied or not.

x−2y+5z=22a−2(21a−1)+5(8a)=2 2a−42a+2+40a=2

And

4x−z=04(2a)−8a=08a−8a=0

Both the equations are satisfied. Therefore, (2a, 21a−1, 8a) is the solution of the given system.

Conclusion:

(2a, 21a−1, 8a) is the solution of the given system.

Chapter 7.3, Problem 40E

Chapter 7.3, Problem 42E

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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