System 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 graph of an inequality represent?

Back

The graph of an inequality represents all the solutions to that inequality. The shaded region indicates the set of points that satisfy the inequality.

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

What does the inequality y < x - 2 represent graphically?

Back

It represents all points below the line y = x - 2, not including the line itself.

Front

How can you solve a system of inequalities by graphing?

Back

To solve by graphing, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

Front

What is the solution set of the system: y < 3 and y > -x + 2?

Back

The solution set is the region where y is less than 3 and greater than -x + 2, which is the area between the two lines.

Front

What does it mean if a point lies outside the shaded region of a graph of inequalities?

Back

If a point lies outside the shaded region, it does not satisfy at least one of the inequalities in the system.

Front

How do you match a system of inequalities to its graph?

Back

To match a system to its graph, identify the boundaries represented by the inequalities and check which graph shows the correct shaded regions.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously, which is the solution to the system.