EXAMPLE 1 Graph a system of two inequalities Graph the system of inequalities. y > –2x – 5 Inequality 1 y < x + 3 Inequality 2.

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Solving Systems of Inequalities by Graphing

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EXAMPLE 1 Graph a system of two inequalities Graph the system of inequalities. y > –2x – 5 Inequality 1 y < x + 3 Inequality 2

EXAMPLE 1 Graph a system of two inequalities STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. SOLUTION STEP 1 Graph each inequality in the system. Use red for y > –2x – 5 and blue for y ≤ x + 3.

EXAMPLE 2 Graph a system with no solution Graph the system of inequalities. 2x + 3y < 6 Inequality 1 y < – x Inequality 2

EXAMPLE 2 Graph a system with no solution STEP 2 Identify the region that is common to both graphs. There is no region shaded both red and blue. So, the system has no solution. SOLUTION STEP Graph each inequality in the system. Use red for 2x + 3y – x + 4.

EXAMPLE 3 Graph a system with an absolute value inequality Graph the system of inequalities. y < 3 Inequality 1 y > x + 4 Inequality 2

EXAMPLE 3 Graph a system with an absolute value inequality STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. SOLUTION STEP 1 Graph each inequality in the system. Use red for y ≤ 3 and blue for y > x + 4.

GUIDED PRACTICE for Examples 1, 2 and 3 Graph the system of inequalities. 1. y < 3x – 2 y > – x + 4

GUIDED PRACTICE for Examples 1, 2 and x – y > x – y < 5

GUIDED PRACTICE for Examples 1, 2 and 3 3. x + y > – 3 –6x + y < 1

GUIDED PRACTICE for Examples 1, 2 and 3 4. y < 4 y > x – 5

GUIDED PRACTICE for Examples 1, 2 and 3 5. y > – 2 y < – x + 2

GUIDED PRACTICE for Examples 1, 2 and 3 6. y > 2 x + 1 y < x + 1 This has no solution.