1/x + 1/y + 1/z = 5. 2/x - 3/y - 4/z = -11. 3/x + 2/y - 1/z = -6. Temukan x + y + z

[tex]
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 5 \\ \frac{2}{x} - \frac{3}{y} - \frac{4}{z} = - 11 \\ \frac{3}{x} + \frac{2}{y} + - \frac{1}{z} = - 6 \\ \\ mis \: \frac{1}{x} = a \: \: \: \frac{1}{y} = b \: dan \: \: \frac{1}{z} = c \\ maka \\ a + b + c = 5 ...1)\\ 2a - 3b - 4c = - 11 ...2)\\ 3a + 2b - c = - 6 ...3)\\ \\ eliminasi \: 1 \: dan \: 2 \\ a + b + c = 5 (kali \: \: 4)\\ 2a - 3b - 4c = - 11 ( kali \: \: 1) \\ \\ 4a + 4b + 4c = 20 \\ \frac{2a - 3b - 4c = - 11}{6a + b = 9 \: \: ...4)} \\ \\ eliminasi \: 1 \: \: dan \: \: 3 \\ a + b + c = 5 \ \\ \frac{3a + 2b - c = - 6 }{4a + 3b = - 1 \: \: ...5)} \\ \\ eliminasi \: 4 \: dan \: 5 \\ 6a + b = 9 (kali \: \: 3)\: \: \\ 4a + 3b = - 1 \: \: (kali \: 1) \\ \\ 18a + 3b = 27\\ \frac{4a + 3b = - 1}{14a = 28} \\ a = \frac{28}{14} = 2 \\ \\ 6a + b = 9 \\ 6(2) + b = 9 \\ 12 + b = 9 \\ b = 9 - 12 = - 3 \\ \\ a + b + c = 5 \\ 2 - 3 + c = 5 \\ c = 6 \\ \frac{1}{x} = a - > \frac{1}{x} = 2 \\ - > x = \frac{1}{2} \\ \frac{1}{y} = b - > \frac{1}{y} = - 3 \\ - > y = \frac{1}{ - 3} \\ \frac{1}{z} = c - > \frac{1}{z} = 6 \\ z = \frac{1}{6} \\ x + y + z = \frac{1}{2} - \frac{1}{3} + \frac{1}{6} \\ - > \frac{3}{6} - \frac{2}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} [/tex]