Systems 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 ordered pairs 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 x and y values of the point into each inequality. If the point 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 or equal to'. It indicates that the value on the left can be greater than or equal to 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 solutions to the entire system.

Front

How do you graph the inequality y < 2x + 3?

Back

To graph y < 2x + 3, first graph the line y = 2x + 3 as a dashed line (indicating that points on the line are not included). Then shade the area below the line.

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

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 overlapping shaded region of the graph.

Front

How can you check if the ordered pair (1, 0) is a solution to the system y ≤ x + 4 and y ≥ 2x - 6?

Back

Substitute x = 1 and y = 0 into both inequalities: 0 ≤ 1 + 4 (true) and 0 ≥ 2(1) - 6 (true). Since both are true, (1, 0) is a solution.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all ordered pairs (x, y) that satisfy all inequalities in the system.