Systems of Linear Inequalities Practice - D

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 set is the region where the graphs of the inequalities overlap.

Front

How do you determine if an ordered pair is a solution to a system of linear inequalities?

Back

To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does it mean for an ordered pair to be in the solution set of a system of linear inequalities?

Back

An ordered pair is in the solution set if it makes all the inequalities in the system true when substituted into them.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the half-plane indicates the region where the inequality holds true.

Front

What is the difference between a solid line and a dashed line in the graph of a linear inequality?

Back

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

Front

How can you find the solution set of a system of linear inequalities graphically?

Back

To find the solution set graphically, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What is the significance of the intersection of half-planes in a system of linear inequalities?

Back

The intersection of half-planes represents the solution set of the system, where all inequalities are satisfied.

Front

What does it mean if an ordered pair is not in the solution set?

Back

If an ordered pair is not in the solution set, it means that substituting the values into the inequalities results in at least one inequality being false.

Front

How do you test an ordered pair to see if it is a solution?

Back

Substitute the x and y values of the ordered pair into each inequality. If all inequalities are satisfied, the pair is a solution.

Front

What is a boundary line in the context of linear inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It separates the solution region from the non-solution region.