The given system of equations are

  x₁ -   x₂ -  7x₃  +  7x₄ = 5

 -x₁ +  x₂ +  8x₃  -   5x₄ = -7

3x₁ - 2x₂ - 17x₃ + 13x₄ = 14

2x₁ -   x₂ - 11x₃ +   8x₄ = 7

We can write above equations are in matrix form as

R indicates Rows

C indicates Columns

R₂ = R₂+R₁

R₃ = R₃-3R₁

R₄ = R₄-2R₁

Interchange R₃ with R₂

R₄ = R₄-R₂

R₄ = R₄+R₃

R₄ = R₄/4

We can write above matrix is in equations form as

x₁ -   x₂ -  7x₃  +  7x₄ = 5           ----------------------------(1)

        x₂ +  4x₃  -  8x₄ = -1          ---------------------------(2)

                  x₃  + 2x₄ = -2          ---------------------------(3)

                            x₄ = -1      ---------------------------(4)

Substitute x₄ = -1 in equation (3)

x₃  + 2(-1) = -2

x₃  = -2 + 2

x₃  = 0

Substitute x₄ = -1 and x₃  = 0  in equation (2)

x₂ +  4(0)  - 8 (-1) = -1

x₂ = -1 - 8

x₂ = -9

Substitute x₂ = -9 , x₄ = -1 and x₃  = 0  in equation (1)

x₁ - (-9) -  7(0) +  7(-1) = 5

x₁ = 5 - 9 + 7

x₁ = 3

Solution :

x₁ = 3

x₂ = -9

x₃  = 0

x₄ = -1