Solutions for the system 10x^2 -y=48 2y=16x^2+48

As long as you're asking for help, you may as well ask a graphing calculator that can actually tell you the answer.

Solutions are (x, y) = (-6, 312) and (6, 312).

_____
Divide the second equation by 2, then substitute the expression for y into the first equation. Solve the quadratic for x.
.. 10x^2 -(8x^2 +24) = 48
.. 2x^2 -72 = 0
.. 2(x -6)(x +6) = 0
.. x = -6 or 6
.. y = 8x^2 +24 = 8*36 +24 = 312 . . . for either value of x