y>1/2x+5 and y<-2x+1

Answer 1

To solve this pair of inequalities, we will graph the two equations:

First inequality: y > (1/2)x + 5

To graph this line, we first plot the y-intercept, which is (0, 5). Then, we find another point by moving one unit to the right and two units up from the y-intercept, giving us (1, 6).

After plotting these two points, we can draw the line passing through them.

Second inequality: y < -2x + 1

To graph this line, we again start with the y-intercept, which is (0, 1). Then, we find another point by moving one unit to the right and two units down from the y-intercept, giving us (1, -1).

After plotting these two points, we draw the line passing through them.

The shaded region where the equations satisfy both inequalities is the area below the line y = (1/2)x + 5 and above the line y = -2x + 1.