EXAMPLE 1 Graph a system of two inequalities

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EXAMPLE 1 Graph a system of two inequalities Graph the system of inequalities. y

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

EXAMPLE 1 Graph a system of two inequalities SOLUTION STEP 1 Graph each inequality

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

EXAMPLE 2 Graph a system with no solution Graph the system of inequalities. 2

EXAMPLE 2 Graph a system with no solution Graph the system of inequalities. 2 x + 3 y < 6 y< – 2 x+4 3 Inequality 1 Inequality 2

EXAMPLE 2 Graph a system with no solution SOLUTION STEP 1 Graph each inequality

EXAMPLE 2 Graph a system with no solution SOLUTION STEP 1 Graph each inequality in the system. Use red for 2 x + 3 y < 6 and blue for y > – 2 x + 4. 3 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.

EXAMPLE 3 Graph a system with an absolute value inequality Graph the system of

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 SOLUTION STEP 1 Graph

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

GUIDED PRACTICE for Examples 1, 2 and 3 Graph the system of inequalities. 1.

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

GUIDED PRACTICE 2. 2 x – 1 y > 4 2 4 x –

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

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

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

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

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

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

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

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

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