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 variables. 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 = 3 (1) − x + 1 2 y + z = 1 2 (2) − x + 2 y + 3 z = 4 (3) Multiply the equation (1) and (2) by 2, and add the equation (1) and (2). 2 x + 2 y + 2 z = 6 − 2 x + y + 2 z = 1 ________________ + 3 y + 4 z = 7 (4) Multiply the equation (2) and (3) by 2, and subtract (2) and (3). − 2 x + y + 2 z = 1 − 2 x + 4 y + 6 z = 8 ________________ − 3 y − 4 z = − 7 (5) Add (4) and (5). + 3 y + 4 z = 7 − 3 y − 4 z = − 7 _________________ 0 = 0 From the above, it can be see that, the system of equation is consistent and infinitely many solutions. Since the equation (4) and (5) are same, just take the equation (4) and assume that z is any real number say t . Now, solve the equation (4) for y in terms of z . 3 y + 4 z = 7 3 y = 7 − 4 z y = 7 − 4 z 3 y = 7 3 − 4 3 z Substitute y = 7 3 − 4 3 z in the equation (1). x + 7 3 − 4 3 z + z = 3 x + 7 3 − 1 3 z = 3 x = 3 − 7 3 + 1 3 z x = 9 3 − 7 3 + 1 3 z That is, x = 2 3 + 1 3 z

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter C.2, Problem 39E

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To solve: The system { x+ y+ z=3−x+12y+ z=12−x+2y+ 3z=4, using the elimination method.

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Chapter C.2, Problem 38E

Chapter C.2, Problem 40E

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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. C.1 - Prob. 54E Ch. C.1 - Prob. 55E Ch. C.1 - Prob. 56E Ch. C.1 - Prob. 57E Ch. C.1 - Prob. 58E Ch. C.1 - Prob. 59E Ch. C.1 - Prob. 60E Ch. C.1 - Prob. 61E Ch. C.1 - Prob. 62E Ch. C.1 - Prob. 63E Ch. C.1 - Prob. 64E Ch. C.1 - Prob. 65E Ch. C.1 - Prob. 66E Ch. C.1 - Prob. 67E Ch. C.1 - Prob. 68E Ch. C.1 - Prob. 69E Ch. C.1 - Prob. 70E Ch. C.1 - Prob. 71E Ch. C.1 - Prob. 72E Ch. C.1 - Prob. 73E Ch. C.1 - Prob. 74E Ch. C.1 - Prob. 75E Ch. C.1 - Prob. 76E Ch. C.1 - Prob. 77E Ch. C.1 - Prob. 78E Ch. C.1 - Prob. 79E Ch. C.1 - Centroid The medians of a triangle are the line...Ch. C.1 - Prob. 81E Ch. C.1 - Prob. 82E Ch. C.1 - Prob. 83E Ch. C.1 - Prob. 84E Ch. C.1 - In this section, we presented two algebraic...Ch. C.1 - Prob. 86E Ch. C.1 - Prob. 87E Ch. C.1 - In the process of solving a system of linear...Ch. C.1 - Prob. 89E Ch. C.1 - Prob. 90E Ch. C.1 - Prob. 91E Ch. C.1 - Prob. 92E Ch. C.1 - Prob. 93E Ch. C.1 - Prob. 94E Ch. C.1 - Prob. 95E Ch. C.1 - Prob. 96E Ch. C.2 - Prob. 1E Ch. 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. C.2 - Prob. 50E Ch. C.2 - Prob. 51E Ch. C.2 - Prob. 52E Ch. C.2 - Prob. 53E Ch. C.2 - Prob. 54E Ch. C.2 - Prob. 55E Ch. C.2 - Prob. 56E Ch. C.2 - Prob. 57E Ch. C.2 - Prob. 58E Ch. C.2 - Prob. 59E Ch. C.3 - Prob. 1E Ch. C.3 - Prob. 2E Ch. C.3 - Prob. 3E Ch. C.3 - Prob. 4E Ch. C.3 - Prob. 5E Ch. C.3 - Prob. 6E Ch. C.3 - Prob. 7E Ch. C.3 - Prob. 8E Ch. C.3 - Prob. 9E Ch. C.3 - Prob. 10E Ch. C.3 - Prob. 11E Ch. C.3 - Prob. 12E Ch. C.3 - Prob. 13E Ch. C.3 - In Problems 13 and 14, solve each system of...Ch. C.3 - Prob. 15E Ch. C.3 - In Problems 15 and 16, solve each system of...Ch. C.3 - Prob. 17E Ch. C.3 - Prob. 18E Ch. C.3 - Prob. 19E Ch. C.3 - Prob. 20E Ch. C.3 - Prob. 21E Ch. C.3 - Prob. 22E Ch. C.3 - Prob. 23E Ch. C.3 - Prob. 24E Ch. C.3 - Prob. 25E Ch. C.3 - Prob. 26E Ch. C.3 - Prob. 27E Ch. C.3 - Prob. 28E Ch. C.3 - Prob. 29E Ch. C.3 - Prob. 30E Ch. C.3 - Prob. 31E Ch. C.3 - Prob. 32E Ch. C.3 - Prob. 33E Ch. C.3 - Prob. 34E Ch. C.3 - Prob. 35E Ch. C.3 - Prob. 36E Ch. C.3 - Prob. 37E Ch. C.3 - Prob. 38E Ch. 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 = 3 − x + 1 2 y + z = 1 2 − x + 2 y + 3 z = 4 , using the elimination method.

Solution Summary: The author explains how to solve the system using the elimination method.

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To solve: The system { x+ y+ z=3−x+12y+ z=12−x+2y+ 3z=4, using the elimination method.

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Chapter C Solutions