Linear Inequalities in Two Variables, terms

Make sure basic inequality and number-line ideas from earlier years are solid first, since linear inequalities in two variables build directly on them. Then learn the y-intercept, which fixes where a line crosses the y-axis, before tackling feasible region, the shaded area that satisfies several inequalities at once.

Students often shade the wrong side of a line, mixing up which region an inequality like y > mx + c actually represents. Another common slip is forgetting that a solid line means the boundary is included (≤ or ≥), while a dashed line means it is excluded (< or >).

Questions typically give two or three inequalities and ask you to shade the region that satisfies all of them, or give a shaded region and ask you to state the inequalities it represents. Watch for the y-intercept and gradient of each boundary line, they decide exactly where and how steeply to draw it.