Question

A system of linear inequalities is shown below.

x + 2y < -5
x - y > 0

Describe the steps to graph the solution set to the system of inequalities. (10 points)

Answer 1

1. Since each inequality has the symbol < or >, not <= or >=, each line will be dashed, not solid.

Answer 2

2. Replace the < or > of each inequality with the = sign.

Answer 3

3. Plot each equation as a line (remember, as a dashed line).

Answer 4

You could put the inequalties in slope point form to make it easier to graph them.

Answer 5

4. Each dashed line separates the plane into 3 regions. The line itself, half-plane to one side of the line and the other half-plane on side of the line.

Answer 6

thank you so much i really appreciate it

Answer 7

5. Using one line, pick a point in one half plane. Test it in that line's inequality. If it works, shade that half plane. If it doesn't work, shade the other half plane.

Answer 8

6. Do the same as step 5. above for the other line and inequality.

Answer 9

7. The graph of the system of inequalities is the part of the plane where the shading of the two inequalities overlaps.

Answer 10

This is just to give you an idea of how it's done. your problem won't look like this.
Plot one dashed line and shade the correct half-plane.

Answer 11

ok thank u

Answer 12

Then plot the other line and its shaded half plane.