It seems like you're working with two inequalities for $y$:

1. $y \geq -x - 5$
2. $y \geq \frac{3}{5}x + 3$

To solve or visualize these inequalities, we can treat them as lines and then shade the region that satisfies both conditions.

Step 1: Graphing the Inequalities

Let's break down the lines these inequalities represent:

• The first inequality $y \geq -x - 5$ corresponds to the line $y = -x - 5$, which has a slope of $-1$ and a y-intercept of $-5$.
• The second inequality $y \geq \frac{3}{5}x + 3$ corresponds to the line $y = \frac{3}{5}x + 3$, which has a slope of $\frac{3}{5}$ and a y-intercept of $3$.

Step 2: Finding the Intersection Point

To find where these two lines intersect, we set the equations equal to each other:

$-x - 5 = \frac{3}{5}x + 3$

Multiplying through by 5 to eliminate the fraction:

$-5x - 25 = 3x + 15$

Now, solve for $x$:

$-5x - 3x = 15 + 25$ $-8x = 40$ $x = -5$

Now, substitute $x = -5$ back into either equation to find $y$:

Using $y = -x - 5$:

$y = -(-5) - 5 = 5 - 5 = 0$

So the two lines intersect at the point $(-5, 0)$.

Step 3: Shading the Region

• For $y \geq -x - 5$, shade the region above the line $y = -x - 5$.
• For $y \geq \frac{3}{5}x + 3$, shade the region above the line $y = \frac{3}{5}x + 3$.

The solution to the system of inequalities will be the region above both lines, including the lines themselves.

---

Do you want more details on graphing or solving inequalities?

Here are 5 related questions you might find useful:

1. How do you graph linear inequalities by hand?
2. What happens when you have a system of inequalities with a different number of variables?
3. How do you interpret the meaning of $y \geq -x - 5$ geometrically?
4. How do you check whether a point satisfies a system of inequalities?
5. What if we had a system involving strict inequalities (like $y > -x - 5$)?

Tip: To graph inequalities with slopes, remember that the line itself represents the equality, and the shading indicates where the inequality holds.