Question

Which graph shows the solution to the system of linear inequalities?

x + 3y > 6

y ≥ 2x + 4

Answer 1

First rewrite each inequality in slope-intercept form:

- x + 3y > 6 → y > −(1/3)x + 2. (boundary y = −(1/3)x + 2 is dashed)
- y ≥ 2x + 4 → y ≥ 2x + 4. (boundary y = 2x + 4 is solid)

The solution is the region that lies above both lines (i.e. above the higher of the two lines at each x). The two lines meet at x = −6/7, y = 16/7; that intersection point does NOT satisfy the first inequality (strict >) so it is excluded.

So pick the graph that:
- has the line y = −(1/3)x + 2 drawn dashed,
- has the line y = 2x + 4 drawn solid,
- and shades the region above both lines (for example, the shading should include the point (0,5) but not the intersection point (−6/7,16/7)).