Solving 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 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 '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

What type of line is used to graph the inequality 'y > -x + 1'?

Back

A dashed line is used to graph the inequality 'y > -x + 1' because the inequality does not include equality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (>, <).

Front

How do you graph the inequality 'y ≥ -2x + 3'?

Back

First, graph the line y = -2x + 3 using a solid line. Then, shade the region above the line to represent all points where y is greater than or equal to -2x + 3.

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where the shaded areas of all inequalities overlap.

Front

How can you check if a point lies in the solution set of a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it lies in the solution set.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.