How many solutions are there to the system of equations $y=-2 x^{2}+2$ and $y=-6$ ? (Enter DNE if the answer doesn't exist.)
Final Answer: \(\boxed{2}\).
Step 1 :The system of equations is given by \(y=-2 x^{2}+2\) and \(y=-6\).
Step 2 :To find the number of solutions, we need to find the number of x-values for which both equations are true.
Step 3 :This means we need to set the two equations equal to each other and solve for x.
Step 4 :Setting \(-2 x^{2}+2 = -6\), we find two solutions for x, which are -2 and 2.
Step 5 :Therefore, there are two points where the two equations intersect.
Step 6 :Final Answer: \(\boxed{2}\).