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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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 >).

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12