Calculate the solution set.

x^2+y^2+8x=-15
9x^2+25y^2=225

My work:
I did elimination...multiplied -25 to the top equation and got..... -16x^2-200x-600...I then used quadratic formula ... And got -7.5 and -5.....
Is -7.5 an EXTRANEOUS SOLUTION because when I plugged -7.5 in for x in -16x^2-200x-600 the result does not equal to +600.

So then the answer is (-5,0) ?
Or is there another way to do this???
How can I check my answer by graphing?
Standard form and then graph it by shifting x and y starting the point of the center?

The tutor was saying

plug -7.5 in for x in +16x^2+200x +600=0, which means that -7.5 is indeed a root of
-16x^2-200x -600=0.

The fallacy lies in the statement:
" plugged -7.5 in for x in -16x^2-200x-600 the result does not equal to +600"
The result should equal to zero (not +600), since you are calculating the left-hand side of the equation.