To check if $(2, 6)$ is a solution to the system of inequalities:

1. Inequality 1: $y < x + 4$

   • Substitute $x = 2$ and $y = 6$: $6 < 2 + 4 \implies 6 < 6$ This is false, because $6$ is not less than $6$.

2. Inequality 2: $x > 2$

   • Substitute $x = 2$: $2 > 2$ This is also false, because $2$ is not greater than $2$.

Since both inequalities are false, the point $(2, 6)$ is not a solution to the system.

Would you like more details on solving systems of inequalities, or have any other questions?

Here are 5 related questions you might consider:

1. How do you solve a system of inequalities graphically?
2. What is the difference between "less than" and "less than or equal to" in inequalities?
3. How do you test if a point satisfies a single inequality?
4. Can a point satisfy only one inequality in a system and still be considered a solution?
5. How does changing the slope or intercept in an inequality affect its graph?

Tip: When testing points in inequalities, always substitute the values directly and compare carefully.