Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a shaded region on one side of a boundary line, which is solid if the inequality includes equality (≥ or ≤) and dashed if it does not (>, <).

Front

What does the symbol '≥' mean in a linear inequality?

Back

'≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

Front

What does the symbol '≤' mean in a linear inequality?

Back

'≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain number.

Front

How do you solve a system of linear inequalities by graphing?

Back

To solve by graphing, graph each inequality on the same coordinate plane, shade the appropriate region for each inequality, and find the overlapping shaded area, which represents the solution set.

Front

What is the solution to the inequality 2x + 3y < 6?

Back

The solution is the set of all points (x, y) that lie below the line 2x + 3y = 6, not including the line itself.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line are included if the inequality is '≥' 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 coordinates of the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).