We are given the system of inequalities:

$y > 2x + 6$

$y < -3x - 4$

We need to check whether the point $(-3, -3)$ satisfies both inequalities.

Step 1: Substitute $(-3, -3)$ into the first inequality

$-3 > 2(-3) + 6$ $-3 > -6 + 6$ $-3 > 0$

This is false.

Step 2: Substitute $(-3, -3)$ into the second inequality

$-3 < -3(-3) - 4$ $-3 < 9 - 4$ $-3 < 5$

This is true, but since the point must satisfy both inequalities and it fails the first one, $(-3,-3)$ is not a solution to the system.

Would you like a graph or further explanation?

Related Questions:

1. How do you determine if a point is a solution to a system of inequalities?
2. What is the graphical representation of this system of inequalities?
3. How do you find the intersection region of two linear inequalities?
4. What are real-world applications of systems of inequalities?
5. How do you determine the feasible region for optimization problems?

Tip:

When checking whether a point satisfies a system of inequalities, always evaluate each inequality separately—all must be true for the point to be a solution.