Solve the following system of equations for the unknown variables.

Add the first two equations: 3y-2z=-8

y+z=-1

Now, multiply the second equation by 2, so 2y+2z=-2. Then, subtract the first equation from the second: y=-8+2, y=-6.

-6+z=-1, z=-1+6=5

And, x equals 3x+3(-6)=3, 3x-18=3, 3x=21, x=7.

Thus, the answer is \((x,y,z)=(3,-2,1).\)

3x + 3y = 3...........................(1)
-3x – 2z = -11.......................(2)
 y + z = -1.............................(3)
 From (3): z = -1 - y                                sub into (2)
3x + 3y =3.............................(1)
-3x -2 (-1 - y)= -11................(4)
-3x + 2 + 2y   = - 11..............(5)
-3x + 2y = - 13......................(6)             add this to (1) above
5y = - 10,
y = -10 / 5 = -2                                        sub this into (3) above:
-2 + z = -1
z =-1 + 2 =1                                            sub this into (2) above
-3x - 2(1) = - 11
-3x = - 9
x =-9 / -3
x = 3 ,     y = -2,     z = 1