Solving Systems of Inequalities(without graphs)

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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the symbol '>' mean in inequalities?

Back

'>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' mean in inequalities?

Back

'<'' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either larger than or equal to the value on the right.

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

Front

How can you solve a system of inequalities without graphing?

Back

You can solve a system of inequalities without graphing by testing points in the inequalities to see if they satisfy all conditions.

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.

Front

If x - y < 2 and x + y < 2, what can you infer about the relationship between x and y?

Back

The inequalities suggest that x is generally less than y plus a small constant, indicating a specific range of values for x and y.

Front

What is the significance of testing points in a system of inequalities?

Back

Testing points helps to identify which points satisfy all inequalities, thus determining the solution set.