Two Variable Inequalities

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form of 'ax + by <, >, ≤, or ≥ c'.

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

To determine if a point (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

The graphical representation of a two-variable inequality is a region on the coordinate plane, often bounded by a line. The line may be solid (for ≤ or ≥) or dashed (for < or >).

If a point lies on the boundary line, it is a solution if the inequality includes equality (≥ or ≤). If the inequality is strict (< or >), the point is not a solution.

'y < mx + b' represents a region above a dashed line, while 'y ≤ mx + b' represents a region above a solid line, including the line itself.

The solution set is identified by shading the region that satisfies the inequality. The direction of shading depends on the inequality sign.