Given the inequalities:
[tex]\begin{gathered} y>-x+3 \\ yIf we plot the two inequalities on a coordinate plane as shown below::[tex]\begin{gathered} y>-x+3\text{ is the red region} \\ y
(a)A point that satisfies both inequalities is (4,0). (Point labelled 1 in the graph)
Check
When x=4, y=0
y >-x+ 3
0 > -4+3
0>-1 (True)
y < x – 1
0<4-1
0<3 (True)
(b)A point that satisfies neither inequality is (0,0) In the white region.
(Point labelled 2 in the graph)
Check
When x=0, y=0
y >-x+ 3
0 > -0+3
0>3 (False)
y < x – 1
0<0-1
0<-1 (False)
(c)A point that satisfies one inequality, but not the other.
The point (0,5)(Point labelled 3a in the graph) satisfies y >-x+ 3 but not y < x – 1.
The point (0,-5) (Point labelled 3b in the graph) satisfies y < x – 1 but not y >-x+ 3.