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 dashed line for < or > and a solid 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 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 ( < 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 significance of the shaded region in the graph of a system of inequalities?

Back

The shaded region represents all possible solutions to the system of inequalities. Any point within this region is a solution.

Front

What does the inequality y ≤ -2x + 5 represent graphically?

Back

It represents all points (x, y) that are below or on the line y = -2x + 5.

Front

What does the inequality y > 2x + 7 represent graphically?

Back

It represents all points (x, y) that are above the line y = 2x + 7.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where their shaded areas overlap. This overlapping region is the solution set.

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on the graph that satisfies all inequalities in the system. It is typically a polygonal shape.