Graphing a System of
Inequalities
System of Inequalities
y  x  5
y  x 1
2
3
We have graphed one inequality at a time.
System of Inequalities
y  x  5
2
2
y


x

5
y   x  5 y  2 x y1 y3 x31x  1
The Solution region is
where the shadings
overlap. For instance
the following point is
in the solution region
because it satisfies
both inequalities:
(0,0)
3
0  0  5
0≤5
True
0  23  0  1
0 > -1
True
Points are solutions to this system if they make both inequalities true.
System of Inequalities
Graph the solution region of the system of inequalities.
y  x 1
y  3x
Plot each inequality individually.
Find out which side to shade for
each inequality.
(0,0)
(0,1)
0  0  1
1  3 0
0≥1
False
1<0
False
Find where the shadings overlap.
System of Inequalities
Graph the solution region of the system of inequalities.
x  y  3
y  4 x  4
Plot each inequality individually.
Find out which side to shade for
each inequality.
(0,0)
(0,0)
0  0  3
0  4  0   4
0<3
True
0≤4
True
Find where the shadings overlap.
System of Inequalities
Graph the solution region of the system of inequalities.
y  x 4
x  4 y  4
Plot each inequality individually.
Find out which side to shade for
each inequality.
(0,0)
(0,0)
0 0 4
0  4  0   4
0≤4
True
0≥4
False
Find where the shadings overlap.
System of Inequalities
Graph the solution region of the system of inequalities.
y  23 x  3
y  23 x
Plot each inequality individually.
Find out which side to shade for
each inequality.
(0,0)
0
2
3
 0  3
0≥3
False
(0,1)
1
2
3
 0
1≤0
False
Find where the shadings overlap.
NO
SOLUTION