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 .