Questions: How many solutions are there to the system of equations (y=-3 x^2+2) and (y=4 x^2+3) ? (Enter DNE if the answer doesn't exist.)

Solution Steps

Given two quadratic equations $y = ax^2 + b$ and $y = cx^2 + d$, we set them equal to each other to get the equation: $(-3 - 4)x^2 + (2 - 3) = 0$.

The discriminant of the equation is calculated as $\Delta = 1$. Since $\Delta > 0$, there are two distinct real solutions. This means the curves intersect at two points.

Final Answer: The number of solutions is 2.