System of Inequalities: Solution or Nah???

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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

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

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

How can 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 solution to the system: y ≤ -2x + 5 and y > 2x + 7?

Back

The solution is the set of points that lie in the overlapping shaded region of the graphs of the two inequalities.

Front

What does the inequality y > -2x + 1 represent graphically?

Back

It represents the region above the line y = -2x + 1, not including the line itself.

Front

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

Back

The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.

Front

How do you identify a point that is NOT a solution to a system of inequalities?

Back

A point that does not satisfy at least one of the inequalities in the system is NOT a solution.

Front

What is the solution to the system: y > -2x + 1 and y ≤ x + 3?

Back

The solution is the set of points that lie in the overlapping shaded region of the graphs of the two inequalities.