Blog: `x + 3w = 4, 2y - z - w = 0, 3y - 2w = 1, 2x - y + 4z = 5` Solve the system of linear equations and check any solutions algebraically.

Sunday, October 1, 2017

$\displaystyle{x}+{3}{w}={4},{2}{y}-{z}-{w}={0},{3}{y}-{2}{w}={1},{2}{x}-{y}+{4}{z}={5}$ Solve the system of linear equations and check any solutions algebraically.

       (equation 1)
      (equation 2)
      (equation 3)
      (equation 4)
Add 1/3 × (equation 1) to equation 2:      (equation 1)
      (equation 2)
      (equation 3)
      (equation 4)Multiply equation...

       (equation 1)
      (equation 2)
      (equation 3)
      (equation 4)
Add 1/3 × (equation 1) to equation 2:
      (equation 1)
      (equation 2)
      (equation 3)
      (equation 4)
Multiply equation 2 by 3:
    (equation 1)
       (equation 2)
       (equation 3)
       (equation 4)
Add 2/3 × (equation 1) to equation 3:
       (equation 1)
       (equation 2)
       (equation 3)
       (equation 4)
Multiply equation 3 by 3:
       (equation 1)
       (equation 2)
       (equation 3)
       (equation 4)
Swap equation 2 with equation 3:
       (equation 1)
       (equation 2)
      (equation 3)
       (equation 4)
Subtract 1/2 × (equation 2) from equation 3:
      (equation 1)
     (equation 2)
       (equation 3)
       (equation 4)
Multiply equation 3 by 2/3:
      (equation 1)
      (equation 2)
      (equation 3)
    (equation 4)
Subtract equation 2 from equation 4:
     (equation 1)
       (equation 2)
       (equation 3)
      (equation 4)
Divide equation 4 by 2:
       (equation 1)
      (equation 2)
   (equation 3)
     (equation 4)
Swap equation 3 with equation 4:
      (equation 1)
      (equation 2)
     (equation 3)
       (equation 4)
Add 1/5 × (equation 3) to equation 4:
      (equation 1)
      (equation 2)
    (equation 3)
     (equation 4)
Multiply equation 4 by -5/8:
       (equation 1)
       (equation 2)
       (equation 3)
      (equation 4)
Subtract 2 × (equation 4) from equation 3:
       (equation 1)
       (equation 2)
       (equation 3)
       (equation 4)
Divide equation 3 by -5:
      (equation 1)
       (equation 2)
      (equation 3)
       (equation 4)
Subtract 9 × (equation 3) from equation 2:
      (equation 1)
     (equation 2)
     (equation 3)
      (equation 4)
Divide equation 2 by 2:
      (equation 1)
       (equation 2)
       (equation 3)
0 w+0 x+0 y+z = 1      (equation 4)
Subtract equation 2 from equation 1:
      (equation 1)
      (equation 2)
      (equation 3)
      (equation 4)
Divide equation 1 by 3:
      (equation 1)
      (equation 2)
     (equation 3)
     (equation 4)

 
w = 1
x = 1
y = 1
z = 1