Is the point (-3, -2) a solution of the intersection of the following set of quadratic equations:
Y < -X^2
X^2 + Y^2 < 16
I'm not sure how to actually work this problem out. Can anyone help me with this problem please.
To determine if the point (-3, -2) is a solution to the intersection of the given set of quadratic equations, you need to check if it satisfies both equations simultaneously. Here's how you can work it out:
1. Equation 1: Y < -X^2
Substitute the values of X and Y into the equation:
-2 < -(-3)^2
Simplify:
-2 < -9
Since this inequality is not true, the point (-3, -2) is not a solution to Equation 1.
2. Equation 2: X^2 + Y^2 < 16
Substitute the values of X and Y into the equation:
(-3)^2 + (-2)^2 < 16
Simplify:
9 + 4 < 16
Since this inequality is true (13 < 16), the point (-3, -2) is a solution to Equation 2.
Since the point does not satisfy both equations simultaneously, it is not a solution to the intersection of the set of quadratic equations.