Solving Systems of Linear Inequalities Graphically

In Quadrant I, both the $x\text{-}$ and $y\text{-}$ values are positive. There are infinitely many systems of inequalities we could write such that their solutions lie in Quadrant I. Here we will show only one of them. Consider the following system. $$\begin{array}{c}\{\begin{array}{ll}y>1& \text{(I)}\\ x>2& \text{(II)}\end{array}\end{array}$$ Graphing the system, we can see that, although the solutions to the individual inequalities lie outside Quadrant I, the solution set to the system is only in Quadrant I.

This is easier to see if we cut away the shading where the inequalities don't overlap.