Explanation Given information: The system of equations 2 ( x + z ) = 6 + x − 3 y 2 x = 11 + y − z x + 2 ( y + z ) = 8 Formula used: Steps to solve a system of three linear equations are as follows: Step 1. Write the equations in standard form. Step 2. Take any two equations and eliminate one of the variables. Step 3. Again take any one of the above equations and the third equation and eliminate the same variable. Step 4. These two equations in two variables can be solved for any one variable by addition or substitution method. Step 5. Substitute the evaluated variable into one of the previous two equations and find the second variable. Step 6. Now that two variables are available, substituting the values of these two in any of the three initial equations will yield the third variable. Calculation: The problem can be solved as follows: Step 1: Write each equation in standard form Ax+By+Cz = D x + 3 y + 2 z = 6 …… (1) 2 x − y + z = 11 …… (2) x + 2 y + 2 z = 8 …… (3) Step 2:Choose a pair of equations and eliminate one of the variables by using addition/subtraction method. Subtracting equation (1) and equation (3) will lead to elimination of x and z x + 3 y + 2 z = 6 x + 2 y + 2 z = 8 − − − − _ y = − 2 Step 3: Substitute y = − 2 in equations (1) and(2) to get the equations in two variables: x + 3 y + 2 z</

6th Edition

ISBN: 9781260673531

Author: Miller, Julie, O'Neill, Molly, Hyde, Nancy

Publisher: McGraw-Hill Education

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Chapter 4, Problem 23T

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To calculate: The linear system of equations

2(x+z)=6+x−3y2x=11+y−zx+2(y+z)=8

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Chapter 4, Problem 22T

Chapter 4, Problem 24T

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The linear system of equations 2 ( x + z ) = 6 + x − 3 y 2 x = 11 + y − z x + 2 ( y + z ) = 8

Solution Summary: The author explains the steps to solve a system of three linear equations.

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To calculate: The linear system of equations

2(x+z)=6+x−3y2x=11+y−zx+2(y+z)=8

Want to see the full answer?

Chapter 4 Solutions

The linear system of equations 2 ( x + z ) = 6 + x − 3 y 2 x = 11 + y − z x + 2 ( y + z ) = 8

Solution Summary: The author explains the steps to solve a system of three linear equations.

Videos

To calculate: The linear system of equations 2(x+z)=6+x−3y2x=11+y−zx+2(y+z)=8

Want to see the full answer?

Chapter 4 Solutions

To calculate: The linear system of equations

2(x+z)=6+x−3y2x=11+y−zx+2(y+z)=8