FASTEST way to solve this system of equations.

[@NkechiR]

Nice

[@cyruschang1904]

x(x + y + z) = 8
y (x + y + z) = -12
z (x + y + z) = 30
x : y : z = 4 : -6 : 15
x = 4a
4a(13a) = 8
a = √(2/13) = (√26)/13
x = 4(√26)/13, y = -6(√26)/13, z = 15(√26)/13

[@NonsoMaths]

Thanks for your comments.
But you made a slight mistake in the solution.
The first line is x(x+y+z)=18 NOT x(x+y+z)=8.
I believe that if you had gotten that line right, your solution would have been correct!
Have a great day!

[@cyruschang1904]

@@NonsoMaths Thank you. Happy Holiday to you, too. In that case:
x : y : z = 3 : -2 : 5
x = 3a
3a(6a) = 18
a = +/- 1
x = 3, y = -2, z = 5
x = -3, y = 2, z = -5

[@NonsoMaths]

Awesome!

[@cyruschang1904]

@@NonsoMaths 😊🙏