Mason is working two summer jobs, making $11 per hour babysitting and making $7 per hour walking dogs. In a given week, he can work at most 16 total hours and must earn a minimum of $140. If xx represents the number of hours babysitting and yy represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.

Let's break down the problem and formulate the system of inequalities.

### Given:
- Mason earns $11 per hour babysitting.
- Mason earns $7 per hour walking dogs.
- He can work at most 16 hours in total.
- He must earn at least $140.

### Variables:
- Let $ x $ represent the number of hours Mason works babysitting.
- Let $ y $ represent the number of hours Mason works walking dogs.

### System of Inequalities:

1. **Time constraint:** Mason can work at most 16 hours in total:
   \[
   x + y \leq 16
   \]

2. **Earnings constraint:** Mason must earn at least $140:
   \[
   11x + 7y \geq 140
   \]

3. **Non-negativity constraints:** The number of hours worked cannot be negative:
   \[
   x \geq 0
   \]
   \[
   y \geq 0
   \]

### Solving Graphically:

1. **Graph the Inequalities**:
   - For $ x + y \leq 16 $, rearrange to $ y \leq 16 - x $. This is a line with a slope of -1, crossing the y-axis at 16.
   - For $ 11x + 7y \geq 140 $, rearrange to $ y \geq \frac{140 - 11x}{7} $. This is a line with a slope of $-\frac{11}{7}$ crossing the y-axis at $\frac{140}{7} = 20$.

2. **Intersection Points**:
   To find the intersection point of the two lines:
   \[
   x + y = 16
   \]
   \[
   11x + 7y = 140
   \]
   Substitute $ y = 16 - x $ into the second equation:
   \[
   11x + 7(16 - x) = 140
   \]
   \[
   11x + 112 - 7x = 140
   \]
   \[
   4x = 28 \implies x = 7
   \]
   Then, $ y = 16 - 7 = 9 $.

   So, the intersection point is $ (7, 9) $.

3. **Possible Solutions**:
   The feasible region is where the inequalities overlap. One possible solution is $ x = 7 $ hours babysitting and $ y = 9 $ hours walking dogs, as this point satisfies both inequalities.

### Conclusion:
One possible solution is that Mason works 7 hours babysitting and 9 hours walking dogs. This way, he works a total of 16 hours and earns exactly $140.

Would you like more details or have any questions?

Here are 5 related questions:
1. What are the other possible values for $ x $ and $ y $ that satisfy the system of inequalities?
2. How would the solution change if Mason had to earn at least $160?
3. How would the inequalities change if Mason could work up to 20 hours per week?
4. Can you find the maximum amount of money Mason could earn under these constraints?
5. How would you graph the inequalities using a software tool like Desmos or GeoGebra?

**Tip**: When solving systems of inequalities graphically, always check the vertices of the feasible region, as they often give optimal solutions.

Learn how to solve a system of linear inequalities graphically, involving a scenario where Mason works babysitting and dog walking jobs to meet minimum earnings and time constraints. Explore the feasible region and find possible solutions.

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