Explanation Given Information: The provide system of equation is, x + y − 3 z = − 1 2 x − y + z = 4 − x − y + z = 1 Formula Used: To solve the system of linear equations, use the elimination method as follows; Step 1: All the equations are written in standard form as A x + B y + C z = D . Step 2: Remove any decimals or fractions. Step 3: Select a variable to eliminate and choose two of the three equations and multiply and add as required, to produce one equation in which the select variable is eliminated. Step 4: Select a different pair of the equations and eliminate the same variables, follow the previous step. Step 5: Solve the system of equations resulting from step (3) and (4). Step 6: Substitute the solution from previous step into one of the original three equations and solve for the third variable. Then check. Calculation: Consider the system of equation, The equations are already in standard form with no fractions or decimals. x + y − 3 z = − 1 …… (1) 2 x − y + z = 4 …… (2) − x − y + z = 1 …… (3) Eliminate the variable y , because the y -terms are opposites of each other in equation (1) and (2) Add the equation (1) and (2) and simplify as follow, x + y − 3 z = − 1 2 x − y − z = 4 _ 3 x − 4 z = 3 Now, Add the equation (1) and (3) and simplify as follow, x + y − 3 z = − 1 − x − y + z = 1 _ − 2 z = 0 And, z = 0 To find the value of x , substitute the value of z = 0 in equation 3 x − 2 z = 3 and simplify the equation, 3 x − 2 z = 3 3 x − 2 ⋅ ( 0 ) = 3 3 x = 3 x = 1 Put the value of x = 1 and z = 0 in equation (3) − x − y + z = 1 − 1 − y + 0 = 1 − y = 1 + 1 y = − 2 Hence, the solution of the provide equation is x = 1 , y = − 2 and z = 0

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ISBN: 9780321877949

Author: Johnson

Publisher: YUZU

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Chapter 12, Problem 6CR

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To calculate: The solution of the systems of linear equations,

x+y−3z=−12x−y+z=4−x−y+z=1

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Chapter 12, Problem 5CR

Chapter 12, Problem 7CR

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The solution of the systems of linear equations, x + y − 3 z = − 1 2 x − y + z = 4 − x − y + z = 1

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To calculate: The solution of the systems of linear equations, x+y−3z=−12x−y+z=4−x−y+z=1

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Chapter 12 Solutions

To calculate: The solution of the systems of linear equations,

x+y−3z=−12x−y+z=4−x−y+z=1