Explanation Given Information: The system of equations: 4 x + 2 z = 12 + 3 y 2 x = 3 x + 3 z − 5 y = 2 x + 7 z + 8 Formula used: To solve a system of three linear equations in three variables Step 1: Write each equation in standard form A x + B y + C z = D . Step 2: Choose a pair of equations and use the addition method to eliminate one of the variables. Step 3: Choose a different pair of equations and eliminate the same variable. Step 4: Now, there are two equations in two variables. Use the substitution or the addition method to solve this system. Step 5: Substitute the values of the variables found in Step 4 into any of the three originalequations that contain the third variable. Solve for the third variable. Step 6: Check the ordered triple in each of the original equations. Calculation: Label the given system of equations as: 4 x + 2 z = 12 + 3 y ………… (1) 2 x = 3 x + 3 z − 5 ………… (2) y = 2 x + 7 z + 8 ………… (3) Step 1: Write equations in standard form A x + B y + C z = D . 4 x − 3 y + 2 z = 12 ………… (4) − x − 3 z = − 5 ………… (5) − 2 x + y − 7 z = 8 ………… (6) Step 2: The y variable can be eliminated from equations (4) and (6). Multiply equation (6) by 3 and add to equation (4) as follows: − 6 x + 3 y − 21 z = 24 4 x − 3 y + 2 z = 12 _ − 2 x − 19 z = 36 ………… (7) Step 3: The x variable can be eliminated from equations (5) and (7). Multiply equation (5) by ( − 2 ) and add to equation (7) as follows: 2 x + 6 z = 10 − 2 x − 19 z = 36 _ − 13 z = 46 Further simplify, z = − 46 13 Step 4: Substitute the above obtained value of z = − 46 13 in equation (5) as follows: − x − 3 z = − 5 − x − 3 ( − 46 13 ) = − 5 − x + 138 13 = − 5 − x = − 5 − 138 13 Further simplify, − x = − 203 13 x = 203 13 Step 5: Substitute the above obtained values of x = 203 13 and z = − 46 13 in equation (4) as follows: 4 x − 3 y + 2 z = 12 4 ( 203 13 ) − 3 y + 2 ( − 46 13 ) = 12 812 13 − 3 y − 92 13 = 12 720 13 − 3 y = 12 Further simplify, − 3 y = 12 − 720 13 − 3 y = − 564 13 y = 188 13 So, from the above calculation the triple ordered pair for the system is ( 203 13 , 188 13 , − 46 13 )

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Chapter 4.5, Problem 17PE

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To calculate: The solution set for the given system of equations:

4x+2z=12+3y2x=3x+3z−5y=2x+7z+8

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Chapter 4.5, Problem 16PE

Chapter 4.5, Problem 18PE

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Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Solve the system by the graphing method. y = − 3 x...Ch. 4.1 - Solve the system by the graphing method. y = 2 x −...Ch. 4.1 - Solve the system by the graphing. 5. Ch. 4.1 - Solve the system by the graphing. 6. Ch. 4.1 - a. A______ of linear equations consists of two or...Ch. 4.1 - For Exercises 2-10, determine if the given point...Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 4PE

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The solution set for the given system of equations: 4 x + 2 z = 12 + 3 y 2 x = 3 x + 3 z − 5 y = 2 x + 7 z + 8

Solution Summary: The author explains how to solve a system of three linear equations in three variables.

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To calculate: The solution set for the given system of equations:

4x+2z=12+3y2x=3x+3z−5y=2x+7z+8

Want to see the full answer?

Chapter 4 Solutions

The solution set for the given system of equations: 4 x + 2 z = 12 + 3 y 2 x = 3 x + 3 z − 5 y = 2 x + 7 z + 8

Solution Summary: The author explains how to solve a system of three linear equations in three variables.

Videos

To calculate: The solution set for the given system of equations: 4x+2z=12+3y2x=3x+3z−5y=2x+7z+8

Want to see the full answer?

Chapter 4 Solutions

To calculate: The solution set for the given system of equations:

4x+2z=12+3y2x=3x+3z−5y=2x+7z+8