tentukan himpunan penyelesaian SPLTV dari x-3y+z=8 , 2x+3y-z=1, 3x-2y-2z= 9

x - 3y + z = 8    --->  z = 3y - x + 8
substitusi
2x + 3y - x =1
2x + 3y - (3y - x + 8) = 1
2x + 3y - 3y + x - 8 = 1
3x = 9
  x = 3
substtusi
3x - 2y - 2z = 9
3x - 2y - 2(3y - x + 8) = 9
3x - 2y - 6y + 2x - 16 = 9
5(3) - 8y - 9 + 16
       - 8y = 10
           y = -1[tex] \frac{1}{4} [/tex]
substitusi
x - 3y + x = 8
3 - 3(-1[tex] \frac{1}{4} [/tex] + z = 8
3 + [tex] \frac{15}{4} [/tex] + z = 8
z = 8 - 3 - 3[tex] \frac{3}{4} [/tex]
z = 1[tex] \frac{1}{4} [/tex]

Himpunan penyelesaian = {3, -1[tex] \frac{1}{4} [/tex], 1[tex] \frac{1}{4} [/tex]}