Question

2x^2 - 3xy-19y^2 = 25, x^2-6y^2 = 250

Answer 1

$2x^2-3xy-19y^2=25\ x^2-6y^2=250\ \ x^2=250+6y^2\ \ 2(250+6y^2)-3sqrt{250+6y^2}y-19y^2=25\ 7y^2+3sqrt{250+6y^2}y=475\ (3sqrt{250y^2+6y^4})^2=(475-7y^2)^2\ 9(250y^2+6y^4)=49y^4-6650y^2+225625\ 2250y^2+54y^4=49y^4-6650y^2+225625\ 5y^4+8900y^2-225625=0\ y^4+1780y^2-45125=0\ y=5\ y=-5\ x=20\ x=-20$