#### Answer

Using Wolfram Mathematica we obtain the following solution to this system of equations:
$$x=0.8;\quad y=1.2;\quad z=-2.4$$

#### Work Step by Step

One of the simplest way to solve a system of linear equations by a computer is using Wolfram Mathematica and the following sequence:
Solve[{120.2 x + 62.4 y - 36.5 z == 258.64,
56.8 x - 42.8 y + 27.3 z == -71.44,
88.1 x + 72.5 y - 28.5 z == 225.88
}, {x, y, z}];
which gives us for the solution:
$$x=0.8;\quad y=1.2;\quad z=-2.4$$