Systems of Inequalities

Front

What is a system of inequalities?

Back

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

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a test point to determine which side of the line to shade, indicating the solution set.

Front

What does it mean for a point to be 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 shaded region of the graph.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

How can you determine if a point is part of the solution set for a system of inequalities?

Back

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

Front

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

Back

The boundary line represents the values where the inequality changes from true to false. If the inequality is strict ('>' or '<'), the line is dashed; if it includes equality ('≥' or '≤'), the line is solid.

Front

What does the solution set of a system of inequalities represent graphically?

Back

The solution set represents the region of the graph where all inequalities overlap, indicating all possible solutions that satisfy the system.

Front

How do you identify a point that is NOT part of the solution set?

Back

A point that does not satisfy at least one of the inequalities in the system is NOT part of the solution set.

Front

What is the role of test points in graphing inequalities?

Back

Test points are used to determine which side of the boundary line to shade when graphing an inequality. If the test point satisfies the inequality, that side is shaded.

Front

What is the graphical representation of the inequality y < mx + b?

Back

The graphical representation is a region below the line y = mx + b, where the line is dashed if the inequality is strict.