2. Steps for Graphing a System of Inequalities
1. Transform each to slope intercept form.
2. Graph each line – make sure it extends across the
entire graph
– Graph a dashed line for < or >
– Graph a solid line for < or >
3. Shade each graph’s less than or greater than area.
Best to shade in two different colors.
– Shade below the line if less than.
– Shade above the line if greater than.
4. The answer is the shaded intersection.
3. Example System Problem #1
y < -2x + 4 and y > 3x – 4
y < -2x + 4 is in
6
yellow. 4
2
y > 3x – 4 is in
blue.
-5 5
-2
The intersection in -4
green is the -6
answer.
4. Example System Problem #2
y ≤ x – 3 and y > -2x +2
y ≤ x – 3 is in
6
yellow. 4
2
y > -2x + 2 is in
blue.
-5 5
-2
The intersection in -4
green is the -6
answer.
5. Example System Problem #3
y > 1 and y ≤ ½x – 2
y > 1 is in yellow.
6
4
2
y ≤ ½x – 2 is in
blue.
-5 5
-2
The intersection in -4
green is the -6
answer.