Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does the symbol '>' represent 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 '<' represent 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 '≥' represent 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 '≤' represent 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 graph the inequality y < 2?

Back

To graph y < 2, draw a horizontal dashed line at y = 2 and shade the area below the line.

Front

How do you graph the inequality y ≥ -x + 3?

Back

To graph y ≥ -x + 3, draw a solid line for y = -x + 3 and shade the area above the line.

Front

What is the solution to the system of inequalities y < 2 and y ≥ -x + 3?

Back

The solution is the region where the shaded areas of both inequalities overlap.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it may or may not be a solution depending on whether the inequality is strict (using < or >) or inclusive (using ≤ or ≥).

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is a solution.