#### Answer

Using Wolfram Mathematica we obtained for the soluton
$$x_1 = -15;\quad x_2 = 40;\quad x_3 = 45;\quad x_4=-75.$$

#### Work Step by Step

One of the simplest ways to solve this system is just using Wolfram Mathematica and the following sequence:
Solve[{x1 + 0.5x2 + 0.33x3 +
0.25x4 == 1.1,
0.5x1 + 0.33x2 + 0.25x3 +
0.21x4 == 1.2,
0.33x1 + 0.25x2 + 0.2x3 +
0.17x4 == 1.3,
0.25x1 + 0.2x2 + 0.17x3 +
0.14x4 == 1.4
}, {x1,x2,x3,x4}];
This yields for the solution of the system:
$$x_1 = -15;\quad x_2 = 40;\quad x_3 = 45;\quad x_4=-75.$$