Solve the system of equations 2x2x2x3x45 x1x2x3x42 3x1x2x32x

Solve the system of equations:

2x₂+x₂-x₃+x₄=5

x₁+x₂+x₃-x₄=2

3x₁-x₂+x₃-2x₄=1

Solution

Given equations:

                           2x₂+x₂-x₃+x₄=5; 3x₂-x₃+x₄=5 --------(1)

                          x₁+x₂+x₃-x₄=2   ----------(2)

                         3x₁-x₂+x₃-2x₄=1   ------------(3)

From eq (1)

                 x3=3x2+x4-5

          substitute this in (2)

x1+x2+(3x2+x4-5)-x4=2; x1+x2+3x2+x4-5-x4=2     

      x1+4x2=7 -------(4)

          and x3 value substitute this in (3)

            3x1-x2+(3x2+x4-5)-2x4=1; 3x1-x2+3x2+x4-5-2x4=1

                                                       3x1+2x2-x4=6 ------(5)

                Now from (4) x1=7-4x2 substitute in (5)

                                      3(7-4x2)+2x2-x4=6

                                      21-12x2+2x2-x4=6

                                       10x2+x4=15

                                     by this subtuteing method we got

   x1=1/7(4x3+9)

   x2=1/7(10-x3)

x3=(7x4-5)/10

          x4=(40x3+5)/7.