Solve the following system of inequalities by graphing.

5x - 4y ≥ -20
3x - 2y ≤ -8
y ≥ -3

I need help, like a website or steps on how to do this. I don't get it, at all.

Graph each inequality as if it were a line like 5x - 4y≥-20 becomes y =5/4 x +5 crosses the y axis at 5 and has a slope of 5/4. Put (0,0) in the inequality y≤5/4x +5 if the inequality is true shade the side of the line that has (0,0) on it. Do the same for the remaining inequalities. For y≥-3 shade above the horizontal line where y = -3.

Okay, thanks. I think i get it

To graph the system of inequalities, you can follow these steps:

1. Start by graphing each individual inequality separately.

For the first inequality, 5x - 4y ≥ -20, you need to rewrite it in slope-intercept form, which is y = mx + b.

Rewrite the inequality as follows:
-4y ≥ -5x - 20
Divide all terms by -4 (which requires flipping the inequality sign):
y ≤ 5/4x + 5

Graph this inequality by:
- Plotting the y-intercept at (0,5).
- Using the slope to find additional points to draw a straight line. In this case, the slope is 5/4, which means that for every 4 units you move to the right, you move up 5 units.

Next, graph the second inequality, 3x - 2y ≤ -8, which can be rewritten in slope-intercept form as follows:
-2y ≤ -3x - 8
Divide all terms by -2 (flipping the inequality sign):
y ≥ 3/2x + 4

Graph this inequality by:
- Plotting the y-intercept at (0,4).
- Using the slope to find additional points. In this case, the slope is 3/2, which means that for every 2 units you move to the right, you move up 3 units.

Lastly, graph the third inequality, y ≥ -3, which is a horizontal line passing through the point (0,-3).

2. Shade the regions that satisfy each inequality.

For the first inequality, y ≤ 5/4x + 5, shade the area below the line because y is less than or equal to the line.

For the second inequality, y ≥ 3/2x + 4, shade the area above the line because y is greater than or equal to the line.

For the third inequality, y ≥ -3, shade above the line because y is greater or equal to -3.

3. Identify the overlapping region or intersection of the shaded areas.

The solution to the system of inequalities is the region where all shaded areas intersect. This is the region that satisfies all the given conditions.

Alternatively, if you prefer an online tool, you can use graphing calculators or websites like Desmos (www.desmos.com) or GeoGebra (www.geogebra.org) to graph and visualize the system of inequalities. These tools can help you plot the lines and shading more accurately.

I hope this explanation helps you understand how to graph and solve a system of inequalities.