LT.6: Students find solution to a system 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 set of all points that satisfy all inequalities in the system.

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 the point satisfies all inequalities, it is a solution.

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 can be less than or equal to the value on the right.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left must be greater than the value on the right.

Front

What is the boundary line in a graph of inequalities?

Back

The boundary line is the line that represents the equality part of the inequality. It divides the graph into two regions: one that satisfies the inequality and one that does not.

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 >).

Front

How do you graph the inequality y < 2x - 1?

Back

To graph y < 2x - 1, first graph the line y = 2x - 1 as a dashed line. Then shade the area below the line to represent all points where y is less than 2x - 1.

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 lies in the shaded region of the graph that satisfies all inequalities in the system.

Front

How can you solve a system of inequalities by graphing?

Back

To solve by graphing, graph each inequality on the same coordinate plane, identify the overlapping shaded region, and that region represents the solution set.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.