Question

Is (4, 10) a solution to this system of inequalities?

y ≤ 10
y > x + 6

Answer 1

To determine if the point (4, 10) is a solution to the system of inequalities, we need to check it against each inequality.

1. **Check the first inequality**: \( y \leq 10 \)

For the point (4, 10), \( y = 10 \).

Substituting into the inequality:
\[
10 \leq 10
\]
This is true.

2. **Check the second inequality**: \( y > x + 6 \)

Again for the point (4, 10), \( y = 10 \) and \( x = 4 \).

Substituting into the inequality:
\[
10 > 4 + 6
\]
This simplifies to:
\[
10 > 10
\]
This is false (10 is not greater than 10).

Since the point (4, 10) satisfies the first inequality but not the second, it is **not** a solution to the system of inequalities.