Two Variable Inequalities

Front

What is a two-variable inequality?

Back

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'.

Front

What does the symbol '>' mean in an inequality?

Back

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.

Front

What does the symbol '<' mean in an inequality?

Back

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.

Front

What does the symbol '≥' mean in an inequality?

Back

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.

Front

What does the symbol '≤' mean in an inequality?

Back

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.

Front

How do you determine if a point is a solution to a two-variable inequality?

Back

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.

Front

What is the graphical representation of a two-variable inequality?

Back

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 >).

Front

What does it mean if a point lies on the boundary line of a two-variable inequality?

Back

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.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'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.

Front

How can you identify the solution set of a two-variable inequality from a graph?

Back

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