Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 5.6, Problem 40E

To determine

To solve: The given system of equations algebraically.

Expert Solution & Answer

Answer to Problem 40E

x=0, y=4, z=−2

Explanation of Solution

Given information: System of equations:

4x+y+2z=03x+4y−2z=20−2x+5y+3z=14

Calculation:

4x+y+2z=0(equation 1)3x+4y−2z=20(equation 2)−2x+5y+3z=14(equation 3)

Start by combining equations 1 and 2 to get,

7x+5y=20(z's cancel out)

Next we want to combine equations 2 and 3 in way to get rid of the z term there also. But we must multiply each equation in such a way as to make that possible.

3(3x+4y−2z=20)⇒ 9x+12y−6z=602(−2x+5y+3z=14)⇒ −4x+10y+6z=28

Combine these

9x+12y−6z=60−4x+10y+6z=28

Gives us:

5x+22y=88

Now we use this equation and the equation we got by combining (1) and (2) to solve for x and y ,

5x+22y=887x+5y=20

To get a common coefficient on the x term the top equation must be multiplied by 7 and the bottom equation by 5.

7(5x+22y=88)=35x+154y=6165(7x+5y=20)=35x+25y=100

Now subtract the bottom row from the top,

35x+154y=616−(35x+25y=100)129y=516y=4

Plugging back into any of the previous equations that only had x and y in it can get us x .

7x+5y=207x+5(4)=20, 7x=0, x=0

Now plug this x and y into one of the three original equations to solve for z , I will use equation (1).

4(0)+4+2z=02x=−4z=−2

Thus, x=0, y=4, z=−2

Chapter 5.6, Problem 39E

Chapter 5.6, Problem 41E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 5.1 - Prob. 1CFU Ch. 5.1 - Prob. 2CFU Ch. 5.1 - Prob. 3CFU Ch. 5.1 - Prob. 4CFU Ch. 5.1 - Prob. 5CFU Ch. 5.1 - Prob. 6CFU Ch. 5.1 - Prob. 7CFU Ch. 5.1 - Prob. 8CFU Ch. 5.1 - Prob. 9CFU Ch. 5.1 - Prob. 10CFU

Ch. 5.1 - Prob. 11CFU Ch. 5.1 - Prob. 12CFU Ch. 5.1 - Prob. 13CFU Ch. 5.1 - Prob. 14CFU Ch. 5.1 - Prob. 15CFU Ch. 5.1 - Prob. 16CFU Ch. 5.1 - Prob. 17CFU Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - 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