Xy+3x+2y=-6

yz+y+3z=-3

xz+2x+z=-2

Find x, y and z

x = - 1 and y = - 3.

y = - 3 and z = - 2.

Step-by-step explanation:

xy+3x+2y=-6 ... (1)

yz+y+3z=-3 ... (2)

xz+2x+z=-2 ... (3)

From the second equation:

yz + y = - 3z - 3

y = (-3z - 3) / (z + 1)

Substitute for y in equation 1:

x (-3z - 3) / (z + 1) + 3x + 2 (-3z - 3) / (z + 1) = - 6

x (-3z - 3) + 3x (z + 1) + 2 (-3x - 3) = - 6 (z + 1)

-3xz - 3x + 3xz + 3x - 6x - 6 = - 6z - 6

-3xz + 3xz - 6x + 6z = 0

- 6x + 6z = 0 ... (4).

From the third equation:

xz + z = - 2x - 2

z = (-2x - 2) / x + 1)

Now substitute for z in equation (4):

-6x + 6 (-2x - 2) / (x + 1) = 0

-6x (x + 1) - 12x - 12 = 0

-6x^2 - 18x - 12 = 0

x^2 + 3x + 2 = 0

(x + 2) (x + 1) = 0

x = - 1, - 2.

Substitute for x in equation 3:

-z - 2 + z = - 2

-2 = - 2

so we cant find z from this value of x.

When x = - 2:

-2z - 4 + z = - 2

-z = 2

z = - 2.

Substitute for x = - 1 in the first equation:

-y - 3 + 2y = - 6

y = - 6 + 3 = - 3.

y = - 3 and z = - 2 satisfies equation 2.