The problem asks us to graph the solution to the system of inequalities: $x + 5y < 15$ $y < 3$

1. Problem Description

The problem asks us to graph the solution to the system of inequalities:

$x + 5y < 15$

$y < 3$

2. Solution Steps

First, we will graph the line $x + 5y = 15$. To do this, we can find two points on the line.

If $x=0$, then $5y=15$, so $y=3$. The point is $(0, 3)$.

If $y=0$, then $x=15$. The point is $(15, 0)$.

Since the inequality is $x + 5y < 15$, we draw a dashed line through $(0,3)$ and $(15,0)$. We need to determine which side of the line to shade. Pick a test point, like $(0,0)$.

$0 + 5(0) < 15$ which means $0 < 15$. Since this is true, we shade the region containing the point $(0,0)$.

Next, we graph the line $y = 3$. Since the inequality is $y < 3$, we draw a dashed horizontal line at $y=3$.

Since the inequality is $y < 3$, we shade the region below the line $y=3$.

The solution to the system of inequalities is the region where the shaded areas overlap.

3. Final Answer

The solution is the region where both inequalities are satisfied. This region is below the line $y=3$ and below the line $x+5y=15$. The lines are dashed.