Question

Solve the system of inequalities by graphing.
x≥
–
6
y>
–
x–6
Select a line to change it between solid and dotted. Select a region to shade it.

Answer 1

The solution set is
{(x,y) : x ≥ −6 and y > −x − 6}.

Graphing instructions:
- Draw the vertical line x = −6 as a solid line (because ≥). Shade the region to the right of that line.
- Draw the line y = −x − 6 as a dashed (open) line (because >). Shade the region above that line.
- The solution is the overlap of those two shaded half-planes: all points to the right of x = −6 that are above the line y = −x − 6.

Note: the two boundary lines meet at (−6, 0). That point is not included because y = 0 does not satisfy y > −x − 6.