Solving Systems by Graphing Unit Assessment: Section 2

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables, representing a region on a graph where all inequalities are satisfied.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Front

What does the solution of a system of inequalities represent?

Back

The solution represents all the points (x, y) that satisfy all inequalities in the system.

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

Substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the inequality y > 2x - 4 represent graphically?

Back

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

Front

What does the inequality y < 2 represent graphically?

Back

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

Front

What is the significance of the point (0, 0) in a system of inequalities?

Back

It is often tested to see if it is a solution; if it satisfies all inequalities, it is part of the solution set.

Front

What does it mean if a point is not a solution to a system of inequalities?

Back

It means that the point does not satisfy at least one of the inequalities in the system.

Front

How do you identify the feasible region in a system of inequalities?

Back

The feasible region is the area where the shaded regions of all inequalities overlap on the graph.