9514 1404 393
Answer:
- see below for a graph
- one possible solution: (12, 5)
Explanation:
I like a graphing calculator for creating graphs. Here, each inequality is in "slope-intercept" form, so the y-intercepts are easily located (+8 and -4).
The slope (x-coefficient) is the "rise" divided by the "run". The boundary line of the first inequality has a rise of -1 for each run of 3 to the right. The second rises 5 units for each 3 to the right. Starting from the y-intercept, additional points to plot are easily found.
Of course, the boundary line is solid for y ≥ ( ), and is dashed for y < ( ). The shading will be above the line (for higher y-values) for the first inequality, and below the line (for lower y-values) for the second inequality. That puts the double-shaded solution area in the right-side quadrant of the X where the lines cross.
There are an infinite number of solution points to choose from. One of them is (12, 5). Points with an x-value that is a multiple of 3 will be easiest to substitute into the inequalities to check.
5 ≥ (-1/3)(12) +8 ⇒ 5 ≥ 4 . . . true
5 < (5/3)(12) -4 ⇒ 5 < 16 . . . true