plug your points into the original two equations. If they satisfy them both, then they are points of intersection.
If x= -5/2 and y= -15/2 then 3x+ y= 3(-5/2)+ (-15/2)= -30/2= -15 so that is correct. [tex]x^2+ y^2= (-5/2)^2+ (-15/2)^2= 25/4+ 225/4= 250/4= 62.5[tex]. No, that's not correct.
If -3x+ y= 15, then y= 15+ 3x. Putting that into the first equation gives or which, dividing by 10, is the same as . Can you solve that? Does it have any real solutions? It is possible that the line completely misses the parabola.