Systems of Inequalities Jones

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 ordered pairs that satisfy all inequalities in the system.

Front

How do you determine if an ordered pair is a solution to a system of 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 the symbol '≤' mean in an inequality?

Back

'≤' 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 '>' mean in an inequality?

Back

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

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region represents the solutions to each inequality. The overlapping region represents the solution to the system.

Front

How do you graph the inequality y ≤ 3x?

Back

To graph y ≤ 3x, first graph the line y = 3x (dashed line) and then shade below the line to indicate all points where y is less than or equal to 3x.

Front

What is the significance of the solution set in a system of inequalities?

Back

The solution set represents all possible ordered pairs that satisfy all inequalities in the system. It shows where the inequalities overlap on a graph.

Front

What does it mean if a point lies outside the solution set of a system of inequalities?

Back

If a point lies outside the solution set, it means that the point does not satisfy at least one of the inequalities in the system.

Front

How can you identify a point that is not a solution to a system of inequalities?

Back

To identify a point that is not a solution, substitute the point's coordinates into each inequality. If it fails to satisfy any inequality, it is not a solution.

Front

What is the difference between 'y < 3x' and 'y ≤ 3x'?

Back

'y < 3x' means that y is strictly less than 3x (not including the line), while 'y ≤ 3x' includes the line (y can be equal to 3x).