Question

How to graph the union of x y<-7 or x-y>6

Answer 1

Graphing the union of the inequalities involves plotting each inequality's boundary line and shading the appropriate side. The union is represented by the combination of shaded regions from both inequalities.

Step-by-step explanation:

To graph the union of the inequalities x + y < -7 and x - y > 6, you would follow these steps:

1. Graph the first inequality x + y < -7. This can be done by first sketching the line x + y = -7, which is the boundary. To find out where to shade for the inequality, pick a test point that is not on the line, like (0,0). As (0) + (0) is not less than -7, you would shade the area opposite to the point (0,0), since that point does not satisfy the inequality.
2. Next, graph the second inequality x - y > 6. Similarly, begin by drawing the line x - y = 6. Using the test point (0,0) again, since (0) - (0) is not greater than 6, you would shade the area opposite to (0,0) since the test point does not meet the inequality.
3. To represent the union of these two inequalities, shade the regions that satisfy either one or both inequalities. Where the shadings overlap represents the values that satisfy both inequalities.

Note that in graphing these inequalities, you will need to label the graph with the equations of the boundaries and choose an appropriate scale for both the x and y axes.