Solve the following system of equations 8x1 6x2 4x3 2 2x1

Solve the following system of equations:                                                                              

                                    8x₁ + 6x₂ – 4x₃ = 2

                                    2x₁ + 4x₂            = 12

                                    6x₁          +2x₃     = 8

Solution

Given that

  8x1 + 6x2 – 4x3  = 2.................................1

  2x1 + 4x2            = 12................................2

  6x1          + 2x3     = 8................................3

Solve equations 1 and 2

Multiply equation 1 with 2

16x1 + 12x2 - 8x3 = 4

12x2 = 4 - 16x1 + 8x3 ...................4

Multiply equation 2 with 3

6x1 + 12x2 = 36

12x2 = 36 - 6x1 .............................5

Equating the equations 4 and 5

  4 - 16x1 + 8x3 = 36 - 6x1

4 - 36 = -6x1 + 16x1 - 8x3

10x1 - 8x3 = -32.............................6

Solve equations 3 and 6

Multiply equation 3 with 2

  6x1          + 2x3     = 8

12x1 + 4x3 = 16

4x3 = 16 - 12x1......................................7

From equation 6

10x1 - 8x3 = -32

10x1 + 32 = 8x3

2( 5x1 + 16) = 2.4x3

4x3 = 5x1 + 16..........................................8

Equating the equations 7 and 8

16 - 12x1 =   5x1 + 16

16 - 16 = 5x1 + 12x1

17x1 = 0

x1 = 0

Substitute x1 in equation 2

2x1 + 4x2            = 12

2( 0 ) + 4x2 = 12

4x2 = 12

x2 = 12 / 4

x2 = 3

Substitute x1 in equation 3

  6x1          + 2x3     = 8

6( 0 ) + 2x3 = 8

2x3 = 8

x3 = 8 / 2

x3 = 4

Therefore,

x1 = 0 , x2 = 3 , x3 = 4