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#32399

systems

inequalities

hard

120 sec

A point $(x, y)$ is a solution to the given system of inequalities in the xy-plane.
$y \geq x - 2$
$y \leq - x + 8$
$x \geq 0$
What is the greatest possible integer value of $x$ for a point $(x, y)$ that is a solution to the given system, if $y$ is also an integer?

• Up to 5 characters (6 if negative). Only numbers, decimal (.), fraction (/), negative (-).
• Fractions must be in lowest terms.
• Mixed numbers must be converted to improper fractions.