How to solve the simultaneous equations? y=-x-3 x=-z-2 y(x+z)=2-xz

We have to solve the system of
equations:

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

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

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

substitute x = -z - 2 in
(1)

=> y = (z + 2) - 3 = z -
1

Substitute x = -z - 2 and y = z - 1 in
(3)

=> (z - 1)(-z - 2 + z) = 2 - (-z -
2)z

=> (z - 1)(-2) = 2 + z^2 +
2z

=> -2z + 2 = 2 + z^2 +
2z

=> z^2 + 4z = 0

=> z(z
+ 4) = 0

=> z = 0 and z = -4

x =
-z - 2 => x = -2 and x = 2

y = z - 1 => y = -1 and y =
-5

The solution for the system is (x, y, z) = (2 , -5
, -4) and (-2 , -1 , 0)