Explanation Given Information: The system of equations: 2 x − 3 y + 2 z = − 1 x + 2 y = − 4 x + z = 1 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 triplet in each of the original equations. Calculation: Label the given system of equations as: 2 x − 3 y + 2 z = − 1 …...…... (A) x + 2 y = − 4 …...…... (B) x + z = 1 …...…... (C) Step 1: The equations are already in standard form. Step 2: The y, z variables can be eliminated from equations A and C. Multiply equation C with ( − 2 ) and add to equation B as follows: − 2 x − 2 z = − 2 2 x − 3 y + 2 z = − 1 _ − 3 y = − 3 y = 1 Step 3: Substitute the above obtained value of y in equation B as follows: x + 2 y = − 4 x + 2 ( 1 ) = − 4 x + 2 = − 4 x = − 4 − 2 Solve it further to get, x

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ISBN: 9781266511486

Author: Miller

Publisher: MCG

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Chapter 4.5, Problem 21PE

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

2x−3y+2z=−1 x+2y =−4 x +z =1

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Chapter 4.5, Problem 20PE

Chapter 4.5, Problem 22PE

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Chapter 4 Solutions

BEGINNING+INTER.ALG.(LL)

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: 2 x − 3 y + 2 z = − 1 x + 2 y = − 4 x + z = 1

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:

2x−3y+2z=−1 x+2y =−4 x +z =1

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Chapter 4 Solutions

The solution set for the given system of equations: 2 x − 3 y + 2 z = − 1 x + 2 y = − 4 x + z = 1

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: 2x−3y+2z=−1 x+2y =−4 x +z =1

Want to see the full answer?

Chapter 4 Solutions

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

2x−3y+2z=−1 x+2y =−4 x +z =1