Graphing Systems of Inequalities

Question

1. Shade the region described by the following system of inequalities. List the vertices (corner points) of this region.

x + y ≥ 2

x + y ≤ 8

2x + y ≤ 10

x ≥ 0, y ≥ 0

Answer 1

x+y>=2 vs 2x+y<=10

subtracting them as equations:

(2x+y)-(x+y)=10-2

2x+y -x-y = 8

x=8

which forces:

y=-6

(8,-6) is the intersection, NOT

in quadrant 1... disqualified

================================

x+y >=8 vs 2x+y <=10

subtracting them as equations:

(2x+y)-(x+y) = 10-8

2x+y-x-y = 2

x=2

which forces y=6

(2,6) is VALID vertex point

the other intercepts are

(2,0)

(5,0)

(0,2)

(0,8)

So the vertices are:

(2,0)

(5,0)

(0,2)

(0,8)

(2,6)

shaded below x+y<=8, below 2x+y<=10, above x+y>=2

and to the right of y-axis

(pentagon)

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