4 = 0.5x*(5-y)^2 and 1 = 0.5x*(3-y)^2
Rearanging both equations, we have
x = 8/(5- y)^2 and x = 2/(3-y)^2
This implies that
8/(5- y)^2 = 2/(3-y)^2 divide both sides by 2
4/(5 - y)^2 = 1/(3-y)^2 cross-multiply and simplify
4(y^2 - 6y + 9) = y^2 - 10y + 25
4y^2 - 24y + 36 = y^2 - 10y + 25
3y^2 - 14y + 11 = 0 factor
(3y -11) (y - 1) = 0 set each factor to 0
y = 11/3 and y = 1
And when y = 11/3, x = 9/2
And when y = 1, x = 1/2
Here's the graph of both x = 8/(5- y)^2 and x = 2/(3-y)^2 and the points of intersection
https://www.desmos.com/calculator/ky62ryvrhs
P.S.- The graphs look as though they might intersect below the y axis at some point.....in fact..they don't !!!