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.

step-by-step explanation:

answer are

step-by-step explanation: