Question

How would you solve the system, y is greater than or equal to x+1
y is less than or eqal to -2x-3

Answer 1

The system of inequalities are  y ≥ x + 1, and   y ≤ - 2x - 3.

1). Draw the coordinate plane.

First inequality is y ≥ x + 1.

2).The graph of the inequality y ≥ x + 1 symbol is ≥, the boundary is included in the solution set. Graph the boundary of the inequality y = x + 1 with solid 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 + 1.

0 ≥ 0 + 1

0 ≥ 1.

The above statement is false.

4).Since the statement is false, shade the region does not contains point (0, 0), Shaded in fuchsia colour.

Second inequality is y ≤ - 2x - 3.

5).The graph of the inequality y ≤ - 2x - 3 symbol is ≤, the boundary is included in the solution set. Graph the boundary of the inequality y = -2x - 3 with solid 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 ≤ - 2x - 3.

0 ≤ - 2(0) - 3

0 ≤ 0 - 3

0 ≤ - 3.

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 + 1 and y ≤ - 2x - 3. This region is shaded in light purple color.