Let's assume $x$ represents the number of packs of printer paper and $y$ represents the number packs of graph paper. Now, we will write an inequality for the number of packs and the cost of packs. Remember that the symbols for at least and at most are $\geq$ and $\leq,$ respectively.

The Number of Packs		The Cost of Packs
Verbal Expression	Algebraic Expression	Verbal Expression	Algebraic Expression
Number of packs of printer paper	$x$	Cost of $x$ packs of printer paper	$$ 2 \cdot x$
Number of packs of graph paper	$y$	Cost of $y$ packs of graph paper	$$ 3 \cdot y$
Add the number of packs of printer and graph paper	$x + y$	Add the costs of packs of printer and graph paper	$$ 2 \cdot x + $ 3 \cdot y$
Setup the inequality	$x + y \geq 6$	Setup the inequality	$$ 2 \cdot x + $ 3 \cdot y \leq $ 27$

Thus, we can form our system of inequalities as the following.

{x + y \geq 6 2 x + 3 y \leq 27 (I) (II)

Now, we will graph the system. Let's start with Inequality I.

Inequality I

In order to graph an inequality, we need a boundary line. The boundary line can be written by replacing the inequality symbol with an equals sign in the inequality as the following.

x + y \geq 6 \Rightarrow x + y = 6

Exercise