The given system of equations are,

Substracting equation (3) from equation (1),

Multiplying equation (2) by 2 and adding it to equation (1),

Multiplying equation (4) with 4 and adding to equation (5),

Substituting the value of y in the equation (4)

Substituting the value of x and y in the equation (1),

Thus, x=-10, y=6 and z=-1 are the required value of all the three variables.