Question

Is (1, 3) a solution to this system of inequalities?

y ≤ x + 2
y ≤ 3

Answer 1

To determine if the point (1, 3) is a solution to the system of inequalities given by:

1. \( y \leq x + 2 \)
2. \( y \leq 3 \)

we need to substitute \( x = 1 \) and \( y = 3 \) into each inequality.

**First inequality:**
\[
y \leq x + 2
\]
Substituting the values:
\[
3 \leq 1 + 2
\]
\[
3 \leq 3
\]
This is true.

**Second inequality:**
\[
y \leq 3
\]
Substituting the values:
\[
3 \leq 3
\]
This is also true.

Since both inequalities are satisfied, the point (1, 3) is indeed a solution to the system of inequalities.