Question

Solve inequalities by graphing: x<1 and y> or equal to -1

Answer 1

Given inequalities are x < 1 and y ≥ -1

Draw the coordinate plane.

Graph the lines x = 1 and y = -1

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  inequalites x < 1 and y ≥ -1

0<1 and 0 ≥ -1

The above statements are true.

shade the regions that contains a point (0,0).

graph of x < 1 shaded with green colour is included the graph of the solution.

The boundary of line graph of x < 1 is solid with fuchsia colour.

graph of y ≥ -1 shaded with purple colour is not included the graph of the solution.

The boundary of the line graph of y ≥ -1 is dotted line with red colour .

The solution of the system is the set of orderd pairs in the intersection of the graph of x < 1 and y ≥ -1.

this region is shaded dark voilet colour.

 

 

Comments

Check the graph.......

Answer 2

The system of inequalities are x <1 and y ≥ - 1.

• Draw a coordinate plane.
• Graph the lines x =1 and y = - 1.
• Since the inequality symbol is < the boundary is not included the solution set.
• Graph the boundary of the inequality x <1 with dotted line.
• Since the inequality symbol is  ≥ the boundary is included the solution set.
• Graph the boundary of the inequality y ≥ - 1 with solid line.
• The graph of x <1 is shaded with teal color and the graph of y ≥ - 1 is shaded with fuchsia color.
• The solution of the system is the set of ordered pairs in the intersection of the graph of this region is shaded in light purple color.

Graph :