What are x,y and z? x+y=-3 x+z=-2 xy+yz+xz=2

Expert Answers

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We have to solve the equations:

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

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

xy + yz + xz = 2 ...(3)

From (1)

x + y = -3

=> y = -3 - x

From (2)

x + z = -2

=> z = -2 - x

Substitute these in (3)

xy + yz + xz = 2

=> x(-3 - x) + (-3 - x)(-2 - x) + x(-2 - x) = 2

=> -3x- x^2 + 6 + 3x + 2x + x^2 - 2x - x^2 = 2

=> - x^2 + 6 = 2

=> x^2 = 4

=> x = 2 and x = -2

y = -3 - x = -5 and -1

z = -2 - x = -4 and 0

The values of x, y and z are (2, -5, -4) and (-2, -1, 0).

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