# Linear Inequalities in Two Variables

I. A First Example (p.313): Exercise #14

II. Basic Ideas:

a. Solution of an inequality is a “region” of

points whose (x,y) coordinates satisfy the

inequality.

b. The “boundary” line is defined by the

equation where the inequality is replaced with

an “=” sign.

c. Determination of the region containing the

solutions is found by “testing” a point not on

the boundary.

d. If a test point’s coordinates satisfy the

inequality then every point in the region will

also, but if they do not then none of the points

in that region will either.

e. The entire set of solutions is indicated by

shading the appropriate region.

III. More Examples (pp.312-313): Exercise #8,12

IV. Boundary Line Convention:

a. For either < or >, the boundary line is a

dashed line indicating its points are not

part of the solution set.

b. For either ≤ or ≥, the boundary line is a

solid line indicating its points are part of

the solution set.

V. A Last Example (p.313): Exercise #22

HW: pp.312-313 / Exercises # 1-17 (odd),21,23