How do you graph the inequality x plus y is greater than 1 and x is less then or equal to y

Question

How do you graph the linear inequality system where x+y>1 and x is less then or equal to y (x,=y).

Answer 1

x+y>1, x≤y need to be written with y on the left:

y>1-x and y≥x.

Now draw graphs of y=1-x and y=x:

Each region corresponds to an inequality. We need the region where y>1-x, that is, above the blue line, and where y≥x, that is, above or on the red line. So the two inequalities are satisfied in R2. Remember to include all the points on the red line in this region but exclude the points on the blue line. In your graph you could shade the region R2 and indicate that the shading doesn’t include the blue line itself but does include the red line.