Question

1. $y < 3$

$y \leq -x + 1$

Explanation:

Step1: Graph $y<3$

Draw a dashed horizontal line at $y=3$, then shade all regions below this line (since $y$ is less than 3, the line is dashed to show it is not included).

Step2: Graph $y\leq -x+1$

First, plot the line $y=-x+1$: this has a y-intercept at $(0,1)$ and a slope of $-1$, so it also passes through $(1,0)$. Draw this as a solid line (since the inequality includes equality, $\leq$). Shade all regions below this line (since $y$ is less than or equal to the expression).

Step3: Find overlapping region

The solution to the system is the area that is shaded in both graphs: the region that is below the dashed line $y=3$ and below the solid line $y=-x+1$.

Answer:

The solution is the overlapping shaded region: all points $(x,y)$ that lie below the solid line $y=-x+1$ (including the line itself) and below the dashed line $y=3$. Visually, this is the area that is under both the solid line $y=-x+1$ and the dashed line $y=3$, with the solid line included and the dashed line excluded.