Inequalities in two variables and regions
Draw a boundary line, make it solid or dashed, test a point and shade the region; then find the region that fits two or three inequalities at once.
- UK: Year 10
- France: grade 7
- Germany: grade 8
- Afghanistan: grade 9
- Syria: grade 9
- Palestine: grade 9
- Ukraine: grade 7
- Russia: grade 9
Guide
An inequality such as y < 2x − 1 is true for a whole region of the plane, not just a line. First draw the boundary y = 2x − 1. Use a dashed line for < or > (points on the line do not count) and a solid line for ≤ or ≥ (they do).
To choose the side, test a point that is not on the line, usually (0, 0). Put it into the inequality: if it is true, (0, 0) is on the solution side; if it is false, the solution is the other side. Do not choose the side that just looks bigger.
In this course you shade the region that satisfies the inequality, as in UK exam papers (some books shade the side that does not satisfy it, so always say which). For several inequalities, the solution is the region that fits all of them at once: where every condition is true, not where just one is.