Question

Graph the solution of the system of linear inequalities.

y ≥ = - x + 2
y ≤ = 3x + 7

coordinates?

Answer 1

To graph the system of linear inequalities, we need to graph each inequality separately and shade the region that satisfies both inequalities.

First, let's graph the inequality y ≥ -x + 2:
1. Start by graphing the line y = -x + 2, which has a y-intercept of 2 and a slope of -1. Mark two points on the line, such as (0, 2) (which is the y-intercept) and (1, 1).
2. Since it is y ≥ -x + 2, we need to shade the region above the line, including the line itself.

Next, let's graph the inequality y ≤ 3x + 7:
1. Start by graphing the line y = 3x + 7, which has a y-intercept of 7 and a slope of 3. Mark two points on the line, such as (0, 7) (which is the y-intercept) and (-1, 4).
2. Since it is y ≤ 3x + 7, we need to shade the region below the line, including the line itself.

Now, let's combine the two shaded regions to find the region that satisfies both inequalities:
1. The region where both shaded regions overlap is the solution to the system of linear inequalities.