The solution is the shaded region below the line y = 1/2x - 2) (excluding the line) and below or on the line y = -2x + 4) (including the line), Option A.
How to graph inequality
First Inequality: y < 1/2x - 2.
This represents a line with a slope of 1/2 and a y-intercept of -2.
The solution to y < 1/2x - 2 is all the points below this line, excluding the line itself.
Second Inequality:y <-2x + 4
This represents a line with a slope of -2 and a y-intercept of 4.
The solution to y <=-2x + 4 is all the points below or on this line.
The combined solution is the overlapping of the shaded regions from both inequalities. It's the region below the first line (excluding the line) and below or on the second line (including the line).
Complete question
Which graph shows the solution to this system of inequalities? Y<1/2x-2. Y<=-2x+4