https://file.aiquickdraw.com/mathbot/file/1727669028294iz44tnvi.jpg

The image contains a system of inequalities and a graph, which shows a feasible region where these inequalities overlap.

The system of inequalities is as follows:

1. \( 5x + 3y \leq 19 \)
2. \( 2y - x \leq 2 \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)

The graph shows the shaded region in the coordinate plane that satisfies all these inequalities. This region will be bounded by the lines representing the linear inequalities.

### Steps to solve this:

1. **Find the lines' equations** by converting the inequalities to equalities:
   - \( 5x + 3y = 19 \)
   - \( 2y - x = 2 \) or \( y = \frac{1}{2}x + 1 \)

2. **Plot the lines** on the graph.
   - For \( 5x + 3y = 19 \), the intercepts can be found:
     - Set \( x = 0 \) to find \( y \)-intercept: \( 3y = 19 \Rightarrow y = \frac{19}{3} \approx 6.33 \).
     - Set \( y = 0 \) to find \( x \)-intercept: \( 5x = 19 \Rightarrow x = \frac{19}{5} \approx 3.8 \).

   - For \( 2y - x = 2 \), rearrange to get the slope-intercept form: \( y = \frac{1}{2}x + 1 \). This line has a slope of \( \frac{1}{2} \) and a \( y \)-intercept of 1.

3. **Find the feasible region** by plotting the shaded region that satisfies all inequalities:
   - The region should be above both lines since \( y \geq 0 \) and \( x \geq 0 \).

4. **Locate the vertices of the feasible region**, which are the points of intersection between these lines and the axes. These points will give you the boundary points of the solution.

Do you need help calculating the intersection points and solving this system further?

Find the region that satisfies the system of inequalities: 2y - x ≤ 2, 5x + 3y ≤ 19, x ≥ 0, y ≥ 0.

Solve the system of inequalities 2y - x ≤ 2 and 5x + 3y ≤ 19, and find the shaded feasible region. Learn the steps to graph these inequalities on the coordinate plane and identify the solution region. Suitable for high school students learning about linear inequalities and graphing.

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