# Calculate the value of x, y and z coordinates given that -360 = -6x + x^2 - 40y + y^2 - 20z + z^2, -600 = -40x + x^2 - 30y + y^2 - 100z + z^2 and 59.85 = -10x + x^2 - 4y + y^2 - 10z + z^2

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Expert Answers

justaguide | Certified Educator

The value of x, y and z has to be determined from the following system of equations:

-360 = -6x + x^2 - 40y + y^2 - 20z + z^2 ...(1)

-600 = -40x + x^2 - 30y + y^2 - 100z + z^2 ...(2)

59.85 = -10x + x^2 - 4y + y^2 - 10z + z^2 ...(3)

(3) - (2)

=> 30x + 26y + 90z = 659.85 ...(4)

(2) - (1)

=> -34x + 10y - 80z = -240 ...(5)

(3) - (1)

=> -4x + 36y+10z = 419.85 ...(6)

(4)+(5)

=> -4x + 36y+10z = 419.85

This is the same as (6)

**As there are 3 variables and only 2 independent equations it is not possible to determine a unique solution.**