Example 4 You have $10 to spend on reprints of a picture you took in Pfeiffer Big Sur State Park. You would like to send one copy to at least 12 friends. Small prints cost $.50 and large prints cost $1. Write and graph a system of inequalities to describe the situation. Then determine two possible combinations of print sizes you can buy. PHOTOGRAPHY Writing a System of Linear Inequalities

Example 4 Writing a System of Linear Inequalities SOLUTION STEP 1 Write a system of inequalities where x is the number of small prints and y is the number of large prints. The number of prints cannot be negative, so you need to include the inequalities and. 0x ≥ 0y ≥ 0x ≥ The number of small prints cannot be negative. 0 y ≥ The number of large prints cannot be negative. You want to send prints to at least 12 friends. yx12+ ≥ You have $10 to spend on the prints. y0.5x10+ ≤

Writing a System of Linear Inequalities Example 4 STEP 2 Graph each inequality in the system. STEP 3Identify the region that is common to all of the graphs. This region is shaded blue in the graph shown at the right. STEP 4Determine how many of each print size you can buy.

Writing a System of Linear Inequalities Example 4 ANSWER Several solutions are possible, such as and as shown at the right. You can buy 10 small prints and 4 large prints, or 16 small prints and 2 large prints. () 10, 4 () 16, 2

Guided Practice 9.WHAT IF? In Example 4, suppose you are given an additional $5 to spend on reprints. Graph the new system of inequalities and give two new possible combinations of print sizes you can buy. for Example 4

Guided Practice for Example 4 ANSWER Sample answers:,. () 10, 6 () 11, 2