Question

How would you show the regions which satisfy (or plot on a graph) the inequality :
x + y < 3
and
x - y > 2

Answer 1

The system of inequalities are x + y < 3, and  x  - y > 2.

1). Draw the coordinate plane.

First inequality is x + y < 3.

Write the inequality  in slope - intercept form y = mx + b.

y < - x + 3

2).The graph of the inequality y < - x + 3 symbol is <, the boundary is not included in the solution set. Graph the boundary of the inequality y = - x + 3 with dotted line.

3).To determine which half - plane to be shaded use a test point in either half - plane.

A simple choice is (0, 0).

Substitute x = 0 and y = 0 in the inequality y < - x + 3.

0  < - 0 + 3

0  < 3.

The above statement is true.

4).Since the statement is true, shade the region contains point (0, 0), Shaded in fuchsia colour.

Second inequality is x  - y > 2.

Write the inequality in slope - intercept form y = mx + b.

- y > - x + 2

y < x - 2.

5).The graph of the inequality y < x - 2 symbol is <, the boundary is not included in the solution set. Graph the boundary of the inequality y = x - 2 with dotted line.

6).To determine which half - plane to be shaded use a test point in either half - plane.

A simple choice is (0, 0).

Substitute x = 0 and y = 0 in the inequality y < x - 2.

0 < 0 - 2

0 < - 2.

The above statement is false.

7).Since the statement is false, shade the region does not contains point (0, 0), shaded in aqua colour.

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of y < - x + 3 and y < x - 2. This region is shaded in light purple color.