graphing systems of Inequalites

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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for 'greater than' or 'less than' and a solid line for 'greater than or equal to' or 'less than or equal to'. Then, shade the appropriate region for each inequality.

Front

What does the shaded region in a graph of inequalities represent?

Back

The shaded region represents all the possible solutions that satisfy the inequality. Points in the shaded area are solutions to the inequality.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What does 'y > 2x - 4' represent graphically?

Back

It represents the region above the line y = 2x - 4, not including the line itself.

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 is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions represents the solution set for the system of inequalities, where all conditions are satisfied.

Front

What does the notation 'y ≤ 3x + 2' indicate?

Back

It indicates that y is less than or equal to 3x + 2, meaning the region below or on the line y = 3x + 2 is included in the solution.

Front

How can you identify a solution set from a graph?

Back

A solution set can be identified by looking for the region where the shaded areas of all inequalities overlap.

Front

What is a boundary line in the context of inequalities?

Back

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