Difficult simultaneous equation?!

x + y = 1

(-9+3sqrt(3))x + (-9-3sqrt(3))y = 0

What is x and y?

Solve by substitution:

x + y = 1 -----> y = 1 - x

Substitute y in second equation with 1 - x

(-9 + 3√3) x + (-9 - 3√3) y = 0
(-9 + 3√3) x + (-9 - 3√3) (1 - x) = 0
(-9 + 3√3) x + (-9 - 3√3) + (9 + 3√3) x = 0
x (-9 + 3√3 + 9 + 3√3) + (-9 - 3√3) = 0
x (6√3) = 9 + 3√3
x = (9 + 3√3) / (6√3)
x = (9 + 3√3) √3 / (6√3√3)
x = (9√3 + 9) / 18
x = (1 + √3) / 2
x = 1/2 + √3/2

y = 1 - x
y = 1 - (1/2 + √3/2)
y = 1/2 - √3/2

Answer:
x = 1/2 + √3/2, y = 1/2 - √3/2

Mαthmφm

x + y = 1
x = 1 - y
substitute 1 - y for x in the other equation:
(-9 + 3√3)(1 - y) + (-9 - 3√3)y = 0
-9 + 3√3 + 9y - 3√3y - 9y - 3√3y = 0
-9 + 3√3 - 6√3y = 0
3√3 - 9 = 6√3y
√3 - 3 = 2√3y
y = (√3 - 3)/(2√3)
x = 1 - (√3 - 3)/(2√3) = (2√3 - √3 + 3)/(2√3) = (√3 + 3)/(2√3)

x + y = 1

(-9+3sqrt(3))x + (-9-3sqrt(3))y = 0
-4.674x-13.327y=0=========> 13.327y= -4.764x ====> y=-0.357x
so if x + y = 1 then x-0.357x=1 or 0.643x=1 =====> x=1.555 and y= -0.555

y=1-x

(-9+3sqrt(3))x + (-9-3sqrt(3))(1-x) = 0
(-9+3sqrt(3))x + (-9-3sqrt(3))+(-x)(-9-3sqrt(3))= 0
-9x+(3sqrt(3))x+9x+(3sqrt(3))x=9+3sqrt…
x=(9+3sqrt(3))/(6sqrt(3))

y=1-(9+3sqrt(3))/(6sqrt(3))

{x = 1/2 + Sqrt[3]/2,

y = (-3 + Sqrt[3])/(2 Sqrt[3])}