Question

or
Is (2, 10) a solution to this system of inequalities?

y ≥ x + 9
y > 3x + 3

Answer 1

To determine if the point (2, 10) is a solution to the given system of inequalities, we'll substitute \( x = 2 \) and \( y = 10 \) into each inequality.

1. For the first inequality \( y \geq x + 9 \):

Substitute \( x = 2 \) into the inequality:

\[
y \geq 2 + 9 \implies y \geq 11
\]

Now, substituting \( y = 10 \):

\[
10 \geq 11 \quad \text{(False)}
\]

2. For the second inequality \( y > 3x + 3 \):

Substitute \( x = 2 \) into the inequality:

\[
y > 3(2) + 3 \implies y > 6 + 3 \implies y > 9
\]

Now, substituting \( y = 10 \):

\[
10 > 9 \quad \text{(True)}
\]

Since (2, 10) does not satisfy the first inequality but does satisfy the second, it is **not** a solution to the system of inequalities.