Question 8.3.3: Sketch the graph of the system {x+y ≤ 4 2x-y ≤ 4...
Sketch the graph of the system
\left\{\begin{array}{r}x+y \leq 4 \\2 x-y \leq 4\end{array}\right.We replace each ≤ with = and then sketch the resulting lines, as shown in Figure 6. Using the test point (0, 0), we see that the solutions of the system correspond to the points below (and on) the line x+y=4 and above (and on) the line 2x-y=4. Shading these half-planes with different colors, as in Figure 6, we have as the graph of the system the points that are in both regions, indicated by the purple portion of the figure.
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