How to graph a system of linear inequalities. How to figure out the points.

y<-5x-7
y>2x+7

Plot the line

y=-5x -7 I assume you know how to do that. Now, since y is less than that line (look at the original equation), the area of allowability is BELOW that line.

Now plot y=2x+7. Since Y is greater than that (see the original equation), the area of interest for this equation is ABOVE that line.

For both equations, the allowed x,y area is where both areas allowed overlap.

To graph a system of linear inequalities, you need to follow these steps:

1. Graph each individual linear inequality by first rewriting it in slope-intercept form (y = mx + b). This form helps identify the slope (m) and y-intercept (b) of the line.

2. Plot the line for each inequality by starting at the y-intercept and then using the slope to identify additional points on the line.

3. Determine the area of allowability for each inequality based on the given conditions (e.g., greater than, less than). This identifies whether the area of interest is above or below the line.

4. Look for the overlapping region between the areas of allowability for all the inequalities. The solution to the system of inequalities will be the shaded region where all the allowable areas overlap.

Now, let's apply these steps to the given system of inequalities:

First, rewrite the inequalities in slope-intercept form:
y < -5x - 7
y > 2x + 7

Next, graph each line and determine the area of allowability for each inequality.

For y < -5x - 7:
- Plot the line with a slope of -5 and a y-intercept of -7.
- The area of allowability is below this line because the given inequality condition is "less than."

For y > 2x + 7:
- Plot the line with a slope of 2 and a y-intercept of 7.
- The area of allowability is above this line because the given inequality condition is "greater than."

Finally, identify the overlapping region. The solution to the system of inequalities will be the area where both areas of allowability overlap. This is the shaded region that satisfies both inequalities.

To determine specific points within the shaded region, you can choose any point within that area and check if it satisfies both inequalities.