Question

Solve the system of inequalities by graphing.
y≤7
y>2x–3
Select a line to change it between solid and dotted. Select a region to shade it.

Answer 1

The solution is the set of points between the two lines y = 2x − 3 and y = 7, including the top boundary and excluding the lower boundary.

Graphing steps:
- Draw the horizontal line y = 7 as a solid line (because y ≤ 7 includes the boundary).
- Draw the line y = 2x − 3 as a dashed (dotted) line (because y > 2x − 3 excludes that boundary).
- Shade the region that lies above the dashed line and at or below the solid line.

In set notation: {(x,y) : 2x − 3 < y ≤ 7}.

Example: (0,0) satisfies 2·0−3 = −3 < 0 ≤ 7, so (0,0) lies in the shaded region.