Q.Solve graphically: $3x - 2y \ge 6$. State whether the boundary line is drawn solid or dashed, and identify which half-plane is the solution using the origin as a test point.

A linear inequality in two variables, such as $2x+y\le10$, is satisfied by an entire region of the coordinate plane rather than a single line. Its boundary line (from the corresponding equation) is drawn solid for a slack inequality ($\le,\ge$) or dashed for a strict one ($<,>$); a convenient test point not on the line — usually the origin — is substituted into the original inequality to decide which of the two half-planes to shade. A system of two-variable inequalities is solved by …