See graph and explanations.
Work Step by Step
Step 1. Based on the given conditions, we can write the first inequality as $x+y\leq4$, shown with the red shaded area. Step 2. The second inequality is $3x+y\leq6$, shown with the blue shaded area in the figure. Step 3. The overlapping area (appears in purple) shows the solution for both inequalities. See graph and explanations.