Q.$x-2y\ge0,\ 2x-y\le-2,\ x\ge0,\ y\ge0$.

A line $ax+by=c$ splits the Cartesian plane into two half-planes. To find which half-plane an inequality $ax+by<c$ (or $>c$) represents: substitute a convenient test point not on the line (usually the origin, when $c\ne0$) into the inequality -- if it holds, shade the half-plane containing that point; if not, shade the other half-plane.

Systems of inequalities. Draw every boundary line, determine each individual half-plane by the test-point method, and the region where every shading overlaps is the graphical solution of the whole system. …