Subtract the 2nd equation from the first: -xy+6y^2=9;
get x in terms of y: x=(6y^2-9)/y;
substitute for x in the 2nd equation: (6y^2-9)^2/y^2+y^2=15;
expand the brackets and multiply through by y^2 to get rid of fraction:
36y^4-108y^2+81+y^4=15y^2; 37y^4-123y^2+81=0.
This equation has no y term, just y^2 and y^4, so it can be solved as a quadratic:
y^2=(123+sqrt(123^2-4*37*81))/74=(123+sqrt(3141))/74=2.4195 or 0.90480, so y=+1.5555 or +0.9512.
Therefore x^2=15-y^2 making x=+3.5469 or +3.7544.
Check: 3.5469^2-3.5469*1.5555+7*1.5555^2=24; 3.5469^2+1.5555^2=15. The other solution doesn't satisfy the original equations, so must be rejected; so x=+3.5469 and y=+1.5555 are the solutions (any combination).