Solve the following system of inequalities graphically

Question

Solve the following system of inequalities graphically
2x+y≥4; x+y≤3;2x–2y<6

Answer 1

Treat each inequality as an equality and graph the lines, find where they intersect.

then shade the areas first above, and then below the 2nd line, and above the 3rd line.

That gives a triangle with vertices (1,2), (3,0) and (2.5, - 0.5) It's a small triangle more in quadrant I, but also in quadrant IV.