Explanation Calculation: Consider the given system of equations, u − 3 4 + v + 1 3 + w − 2 8 = 1 â€¦â€¦ (1) u − 3 2 + v + 1 2 + w − 2 4 = 0 â€¦â€¦ (2) u − 3 4 − v + 1 2 + w − 2 2 = − 6 â€¦â€¦ (3) Let x = u − 3 , y = v + 1 and z = w − 2 . Then, Equation (1) becomes, x 4 + y 3 + z 8 = 1 Simplify the above equation, 6 x + 8 y + 3 z 24 = 1 6 x + 8 y + 3 z = 24 Consider the above equation as, 6 x + 8 y + 3 z = 24 â€¦â€¦ (4) Equation (2) becomes, x 2 + y 2 + z 4 = 0 Simplify the above equation, 2 x + 2 y + z 4 = 0 2 x + 2 y + z = 0 Consider the above equation as, 2 x + 2 y + z = 0 â€¦â€¦ (5) Equation (3) becomes, x 4 − y 2 + z 2 = − 6 Simplify the above equation, x − 2 y + 2 z 4 = − 6 x − 2 y + 2 z = − 6 4 x − 2 y + 2 z = − 24 Consider the above equation as, x − 2 y + 2 z = − 24 â€¦â€¦ (6) Now eliminate the variable y from the equations (4) and (6). Then multiply equation (6) by 4 and add it to equation (4). 4 x − 2 y + 2 z = 4 − 24 4 x − 8 y + 8 z = − 96 So, 6 x + 8 y + 3 z = 24 4 x − 8 y + 8 z = − 96 ¯ 10 x + 11 z = − 72 Consider above equation as, 10 x + 11 z = − 72 â€¦â€¦ (7) Now eliminate the variable y from the equations (5) and (6). Add equation (5) and equation (6) to eliminate y as, 2 x + 2 y + z = 0 x − 2 y + 2 z = − 24 ¯ 3 x + 3 z = − 24 Take 3 common on both sides and rewrite the equation as, x + z = − 8 â€¦â€¦ (8) Now eliminate the variable x from equation (7) and equation (8), Multiply equation (8) with − 10 and add it to equation (8), − 10 x + z = − 10 − 8 − 10 x − 10 z = 80 So, 10 x + 11 z = − 72 − 10 x − 10 z = 80 ¯ z = 8 Now, substitute the value z = 8 into equation (8) to solve for x as, x + 8 = − 8 x = − 8 − 8 x = − 16 Now, substitute the value x = − 16 and z = 8 into equation (5) to solve for y as, 2 − 16 + 2 y + 8 = 0 − 32 + 2 y + 8 = 0 2 y = 32 − 8 2 y = 24 Further simplify for y , y = 24 2 y = 12 Hence, x = − 16 , y = 12 and z = 8

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Chapter 8.2, Problem 63PE

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To calculate: The solution set of the system of equations

u−34+v+13+w−28=1u−32+v+12+w−24=0u−34−v+12+w−22=−6

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Chapter 8.2, Problem 62PE

Chapter 8.2, Problem 64PE

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The solution set of the system of equations u − 3 4 + v + 1 3 + w − 2 8 = 1 u − 3 2 + v + 1 2 + w − 2 4 = 0 u − 3 4 − v + 1 2 + w − 2 2 = − 6

Solution Summary: The author explains how to calculate the solution set of the system of equations lu-34+

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To calculate: The solution set of the system of equations

u−34+v+13+w−28=1u−32+v+12+w−24=0u−34−v+12+w−22=−6

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Chapter 8 Solutions

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The solution set of the system of equations u − 3 4 + v + 1 3 + w − 2 8 = 1 u − 3 2 + v + 1 2 + w − 2 4 = 0 u − 3 4 − v + 1 2 + w − 2 2 = − 6

Solution Summary: The author explains how to calculate the solution set of the system of equations lu-34+

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To calculate: The solution set of the system of equations u−34+v+13+w−28=1u−32+v+12+w−24=0u−34−v+12+w−22=−6

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Chapter 8 Solutions

Additional Math Textbook Solutions

To calculate: The solution set of the system of equations

u−34+v+13+w−28=1u−32+v+12+w−24=0u−34−v+12+w−22=−6