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solve: x + y = 5xy and y + z = 7yz and z + x = 6xz
Solution
x + y = 5xy and y + z = 7yz and z + x = 6xz
=> 1/x + 1/y = 5 ....eq1
1/y + 1/z = 7 ....eq2
1/x + 1/z = 6 ,....eq3
eq3 - eq1 =>
1/z - 1/y = 1 ....eq4
eq2 + eq4
=> 2/z = 8
=> z = 1/4
so 1/y = 1/z -1 = 3
so y = 1/3
from eq1 , 1/x + 3 = 5
=> 1/x = 2
=> x = 1/2

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solve-x+ y - 5xyand y + z - 7yzand z + x - 6xzSolutionx + y - 5xy and.docx

  • 1. solve: x + y = 5xy and y + z = 7yz and z + x = 6xz Solution x + y = 5xy and y + z = 7yz and z + x = 6xz => 1/x + 1/y = 5 ....eq1 1/y + 1/z = 7 ....eq2 1/x + 1/z = 6 ,....eq3 eq3 - eq1 => 1/z - 1/y = 1 ....eq4 eq2 + eq4
  • 2. => 2/z = 8 => z = 1/4 so 1/y = 1/z -1 = 3 so y = 1/3 from eq1 , 1/x + 3 = 5 => 1/x = 2 => x = 1/2