Using graphing, pick any coordinate that is a possible solution to the system of inequalities.
2y > x + 2
4y < 5x +4
One possible solution to this system of inequalities is the coordinate (4, 2).
First, let's graph the inequality 2y > x + 2. This is equivalent to y > 0.5x + 1. We will plot this line as a dashed line because the inequality is strictly greater than, and all points above this line will satisfy the inequality.
Next, let's graph the inequality 4y < 5x + 4. This is equivalent to y < 1.25x + 1. We will plot this line as a dashed line because the inequality is strictly less than, and all points below this line will satisfy the inequality.
The point (4, 2) is a solution because it lies within the shaded region where both inequalities are simultaneously satisfied.
Here is an illustration of the graph with the point (4, 2) as a possible solution:
graph
{x>0.5y+1,
y<1.25x+1,
x=4,
y=2}