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Solve: x + y + z = 4, x + y - z = 8 and x - y + z = 1

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theta123 | Student, Kindergarten | (Level 1) Salutatorian

Posted June 7, 2012 at 4:33 PM via web

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Solve: x + y + z = 4, x + y - z = 8 and x - y + z = 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 7, 2012 at 4:40 PM (Answer #1)

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The set of equations to be solved is:

x + y + z = 4 ...(1)

x + y - z = 8 ...(2)

x - y + z = 1 ...(3)

(1) + (2)

=> x + y = 6

=> x = 6 - y

substitute in (3)

6 - y - y + z = 1

=> z = 2y - 5

Substitute for x and z in (2)

=> 6 - y + y - 2y + 5 = 8

=> 2y = 3

=> y = 3/2

x = 6 - y = 6 - 3/2 = 4.5

z = -2

The solution of the system of equations is x = 4.5, y = 1.5 and z = -2

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