Question

Which graph represents the following system of inequalities? y>(1)/(2)x-1 y<=-x+1 y>-2x-1

Answer 1

? We don't see any graphs to choose from

Explanation:

`y>(1)/(2)x-1` Graph a dotted line (to show it's not included) with y-intercept 1 and slope 1/2. Test the origin (0, 0) in the inequality:

`0 > (1)/(2)0 - 1 = -1` This is true, so shade the side of the line that the origin is on (above the line).

Next inequality...

`y \le x+1` Graph a solid line with y=intercept 1 and slope 1. Test the origin.

`0 \le 0+1=1` True! Shade the side of the line the origin is on (below the line). See image2, attached.

`y>-2x-1` Graph a dotted line with y-intercept -1 and slope -2. Test the origin (0, 0).

`0>-2(0)-1=-1` True, so shade the side the origin is on (above the line).

The solutions are located where all the shadings intersect. See image3. The solutions are above the red line, above the green line and below the blue line.