Explanation Procedure used: Step 1: Selected two of the equations and eliminate one of the variables from one of the equations. Select any two other equations and eliminate the same variable from one of the equations. Step 2: This will leave two equations with two unknowns. Solve this system by eliminating one of the variable. Step 3: User the two known values of the variables found in step 2 to find the values of the third variable. Step 4: Check the answer. Calculation: Consider the equations x + y + z + w = 0 (1) 2 x − 3 y − z + w = − 17 (2) 3 x + y + 2 z − w = 8 (3) − x + 2 y − 3 z + 2 w = − 7 (4) Add the equations (1) and (4). x + y + z + w = 0 − x + 2 y − 3 z + 2 w = − 7 _____________________ 3 y − 2 z + 3 w = 7 (5) Multiply the equation (4) by 2, then add the equations (2) and (4). 2 x − 3 y − z + w = − 17 − 2 x + 4 y − 6 z + 4 w = − 14 _____________________ y − 7 z + 5 w = − 31 (6) Multiply the equation (4) by 3, then add the equations (3) and (4). 3 x + y + 2 z − w = 8 − 3 x + 6 y − 9 z + 6 w = − 21 _____________________ 7 y − 7 z + 5 w = − 13 (7) Multiply the equation (6) by −3 and subtract the equation (5) and (6). − 3 y + 21 z − 15 w = 93 3 y − 2 z + 3 w = − 7 ____________________ + 19 z − 12 w = − 86 That is, 19 z − 12 w = − 86 (8) Multiply the equation (6) by −7 and add the equation (6) and (7). − 7 y + 49 z − 35 w = 217 7 y − 7 z + 5 w = − 13 ____________________ + 42 z − 30 w = 204 (9) Multiply the equation (8) and (9) by 5 and −2, respectively and subtract the equation (8) and (9). 95 z − 60 w = 430 − 84 z + 60 w = − 408 ____________________ 11 z = 22 That is, z = 2

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter C.2, Problem 56E

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To solve: The system { x+ y+ z+ w=02x−3y− z+ w=−173x+ y+2z− w=8−x+2y−3z+2w=−7, find the value of x, y, z and w.

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Chapter C.2, Problem 55E

Chapter C.2, Problem 57E

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Chapter C Solutions

Elementary & Intermediate Algebra

Ch. C.1 - A___ ___ ___ ___ is a grouping of two or more...Ch. C.1 - A____ of a system of equations consists of values...Ch. C.1 - Prob. 3E Ch. C.1 - Prob. 4E Ch. C.1 - Prob. 5E Ch. C.1 - True or False A system of two linear equations...Ch. C.1 - Prob. 7E Ch. C.1 - Prob. 8E Ch. C.1 - Prob. 9E Ch. C.1 - Prob. 10E

Ch. C.1 - Prob. 11E Ch. C.1 - Prob. 12E Ch. C.1 - Prob. 13E Ch. C.1 - Prob. 14E Ch. C.1 - Prob. 15E Ch. C.1 - Prob. 16E Ch. C.1 - 17.While a system of equations is solved, a false...Ch. C.1 - Prob. 18E Ch. C.1 - Prob. 19E Ch. C.1 - Prob. 20E Ch. C.1 - Prob. 21E Ch. C.1 - In Problems 2022, solve the system. Draw a graph...Ch. C.1 - Prob. 23E Ch. C.1 - Prob. 24E Ch. C.1 - Prob. 25E Ch. C.1 - Prob. 26E Ch. C.1 - Prob. 27E Ch. C.1 - Prob. 28E Ch. C.1 - Prob. 29E Ch. C.1 - Prob. 30E Ch. C.1 - Prob. 31E Ch. C.1 - Prob. 32E Ch. C.1 - Prob. 33E Ch. C.1 - Prob. 34E Ch. C.1 - Prob. 35E Ch. C.1 - Prob. 36E Ch. C.1 - In Problems 3542, solve the system of equations...Ch. C.1 - Prob. 38E Ch. C.1 - Prob. 39E Ch. C.1 - Prob. 40E Ch. C.1 - Prob. 41E Ch. C.1 - Prob. 42E Ch. C.1 - Prob. 43E Ch. C.1 - Prob. 44E Ch. C.1 - Prob. 45E Ch. C.1 - Prob. 46E Ch. C.1 - Prob. 47E Ch. C.1 - Prob. 48E Ch. C.1 - Prob. 49E Ch. C.1 - Prob. 50E Ch. C.1 - Prob. 51E Ch. C.1 - Prob. 52E Ch. C.1 - Prob. 53E Ch. 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C.2 - A _______ to a system of equations consists of...Ch. C.2 - Prob. 3E Ch. C.2 - Prob. 4E Ch. C.2 - Prob. 5E Ch. C.2 - Prob. 6E Ch. C.2 - Prob. 7E Ch. C.2 - Prob. 8E Ch. C.2 - Prob. 9E Ch. C.2 - Prob. 10E Ch. C.2 - Prob. 11E Ch. C.2 - Prob. 12E Ch. C.2 - Prob. 13E Ch. C.2 - Prob. 14E Ch. C.2 - Prob. 15E Ch. C.2 - Prob. 16E Ch. C.2 - Prob. 17E Ch. C.2 - Prob. 18E Ch. C.2 - Prob. 19E Ch. C.2 - Prob. 20E Ch. C.2 - Prob. 21E Ch. C.2 - Prob. 22E Ch. C.2 - Prob. 23E Ch. C.2 - Prob. 24E Ch. C.2 - Prob. 25E Ch. C.2 - Prob. 26E Ch. C.2 - Prob. 27E Ch. C.2 - Prob. 28E Ch. C.2 - Prob. 29E Ch. C.2 - Prob. 30E Ch. C.2 - Prob. 31E Ch. C.2 - Prob. 32E Ch. C.2 - Prob. 33E Ch. C.2 - Prob. 34E Ch. C.2 - Prob. 35E Ch. C.2 - Prob. 36E Ch. C.2 - Prob. 37E Ch. C.2 - Prob. 38E Ch. C.2 - Prob. 39E Ch. C.2 - Prob. 40E Ch. C.2 - Prob. 41E Ch. C.2 - Prob. 42E Ch. C.2 - Prob. 43E Ch. C.2 - Prob. 44E Ch. C.2 - Prob. 45E Ch. C.2 - Prob. 46E Ch. C.2 - Prob. 47E Ch. C.2 - Prob. 48E Ch. C.2 - Prob. 49E Ch. 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C.3 - Prob. 39E Ch. C.3 - Prob. 40E Ch. C.3 - Prob. 41E Ch. C.3 - In Problems 39-44, solve each system of equations...Ch. C.3 - Prob. 43E Ch. C.3 - Prob. 44E Ch. C.3 - Prob. 45E Ch. C.3 - Prob. 46E Ch. C.3 - Prob. 47E Ch. C.3 - Prob. 48E Ch. C.3 - Prob. 49E Ch. C.3 - Prob. 50E Ch. C.3 - Prob. 51E Ch. C.3 - Prob. 52E Ch. C.3 - Prob. 53E Ch. C.3 - Prob. 54E Ch. C.3 - In Problems 51-56, an augmented matrix of a system...Ch. C.3 - In Problems 51-56, an augmented matrix of a system...Ch. C.3 - Prob. 57E Ch. C.3 - Prob. 58E Ch. C.3 - Prob. 59E Ch. C.3 - Prob. 60E Ch. C.3 - Prob. 61E Ch. C.3 - Prob. 62E Ch. C.3 - Prob. 63E Ch. C.3 - Prob. 64E Ch. C.3 - Prob. 65E Ch. C.3 - Prob. 66E Ch. C.3 - In Problems 57-78, solve each system of equations...Ch. C.3 - Prob. 68E Ch. C.3 - Prob. 69E Ch. C.3 - Prob. 70E Ch. C.3 - Prob. 71E Ch. C.3 - Prob. 72E Ch. C.3 - Prob. 73E Ch. C.3 - Prob. 74E Ch. C.3 - Prob. 75E Ch. C.3 - Prob. 76E Ch. C.3 - Prob. 77E Ch. C.3 - In Problems 45-50, solve each system of equations...Ch. C.3 - Prob. 79E Ch. C.3 - Prob. 80E Ch. C.3 - Finance Carissa has 20,000 to invest. Her...Ch. C.3 - Prob. 82E Ch. C.3 - Prob. 83E Ch. C.3 - Prob. 84E Ch. C.3 - Prob. 85E Ch. C.3 - Prob. 86E Ch. C.3 - Prob. 87E Ch. C.3 - Prob. 88E Ch. C.3 - Prob. 89E Ch. C.3 - Prob. 90E Ch. C.3 - Graphing calculators have the ability to solve...Ch. C.3 - Prob. 92E Ch. C.3 - Prob. 93E Ch. C.3 - Graphing calculators have the ability to solve...Ch. C.4 - D = |abcd| = _____________.Ch. C.4 - Prob. 2E Ch. C.4 - Prob. 3E Ch. C.4 - Prob. 4E Ch. C.4 - Prob. 5E Ch. C.4 - In Problems 5 and 6, use Cramers Rule to solve the...Ch. C.4 - Prob. 7E Ch. C.4 - Prob. 8E Ch. C.4 - Prob. 9E Ch. C.4 - Prob. 10E Ch. C.4 - Prob. 11E Ch. C.4 - Prob. 12E Ch. C.4 - Prob. 13E Ch. C.4 - Prob. 14E Ch. C.4 - Prob. 15E Ch. C.4 - Prob. 16E Ch. C.4 - Prob. 17E Ch. C.4 - Prob. 18E Ch. C.4 - In Problems 15-22, solve each system of equations...Ch. C.4 - Prob. 20E Ch. C.4 - Prob. 21E Ch. C.4 - Prob. 22E Ch. C.4 - Prob. 23E Ch. C.4 - Prob. 24E Ch. C.4 - Prob. 25E Ch. C.4 - Prob. 26E Ch. C.4 - Prob. 27E Ch. C.4 - Prob. 28E Ch. C.4 - Prob. 29E Ch. C.4 - Prob. 30E Ch. C.4 - Prob. 31E Ch. C.4 - Prob. 32E Ch. C.4 - Prob. 33E Ch. C.4 - Prob. 34E Ch. C.4 - Prob. 35E Ch. C.4 - Prob. 36E Ch. C.4 - Prob. 37E Ch. C.4 - Prob. 38E Ch. C.4 - Prob. 39E Ch. C.4 - Prob. 40E Ch. C.4 - Prob. 41E Ch. C.4 - Prob. 42E Ch. C.4 - Prob. 43E Ch. C.4 - Prob. 44E Ch. C.4 - Prob. 45E Ch. C.4 - Prob. 46E Ch. C.4 - Prob. 47E Ch. C.4 - Prob. 48E Ch. C.4 - Problems 4750, use the following result....Ch. C.4 - Prob. 50E Ch. C.4 - Prob. 51E Ch. C.4 - Prob. 52E Ch. C.4 - Prob. 53E Ch. C.4 - Prob. 54E Ch. C.4 - Prob. 55E Ch. C.4 - In Problems 5560, use technology to solve the...Ch. C.4 - Prob. 57E Ch. C.4 - In Problems 5560, use technology to solve the...Ch. C.4 - Prob. 59E Ch. C.4 - Prob. 60E

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The system { x + y + z + w = 0 2 x − 3 y − z + w = − 17 3 x + y + 2 z − w = 8 − x + 2 y − 3 z + 2 w = − 7 , find the value of x , y , z and w .

Solution Summary: The author explains how to solve the system by eliminating one of the variables from one equation.

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To solve: The system { x+ y+ z+ w=02x−3y− z+ w=−173x+ y+2z− w=8−x+2y−3z+2w=−7, find the value of x, y, z and w.

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Chapter C Solutions