\(5x^2-45y^2-30y-5\\ =5\left(x^2-\left(9y^2+6y+1\right)\right)\\ =5\left[x^2-\left(3y+1\right)^2\right]\\ =5\left(x+3y+1\right)\left(x-3y-1\right)\)

\(a\times\dfrac{1}{5}+\dfrac{3}{10}+\dfrac{1}{2}\times a=500\\ a\times\left(\dfrac{1}{5}+\dfrac{1}{2}\right)=500-\dfrac{3}{10}\\ a\times\dfrac{7}{10}=\dfrac{4997}{10}\\ a=\dfrac{4997}{7}\)

\(y\times\dfrac{1}{2}+y:\dfrac{2}{3}=5\\ y\times\dfrac{1}{2}+y\times\dfrac{3}{2}=5\\ y\times2=5\\ y=\dfrac{5}{2}\)