To determine if the point \((0, 3)\) is a solution for the given system of inequalities, we will check it against each inequality.
Inequality 1: \(x \leq 5\)
For the point \((0, 3)\):
\(0 \leq 5\) → This is true.
Inequality 2: \(y > -2x + 3\)
Substituting \(x = 0\) and \(y = 3\):
\(3 > -2(0) + 3\)
\(3 > 0 + 3\)
\(3 > 3\) → This is false.
Since the point \((0, 3)\) satisfies Inequality 1 but does not satisfy Inequality 2, we can conclude that:
The point (0, 3) is not a solution for this system of linear inequalities.