Solve one-variable linear and compound inequalities using equivalent operations, reversing the inequality when multiplying or dividing by a negative, and represent solutions with number lines, intervals, or set notation. Solve two-variable systems of linear equations algebraically and graphically, including systems with unique, no, or infinitely many solutions, and solve linear–quadratic systems by substitution or graphing to identify zero, one, or two real intersection points. Graph linear inequalities and systems as half-planes with correctly included or excluded boundaries, interpret their intersections as feasible regions and solution sets, and use ordered pairs, units, and relevant corner points to assess feasible choices.