Solving Systems of Inequalities

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

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies each inequality. 4. The solution is where the shaded regions overlap.

Front

What does the solution to a system of inequalities represent?

Back

The solution represents all the points (x, y) that satisfy all inequalities in the system, often visualized as a shaded region on a 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 do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graph will have a dashed line for y = 2x - 4, and the region above the line will be shaded.

Front

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

Back

It represents a solid line for y = 2x - 1, with the region below the line shaded, including the line itself.

Front

How can you identify the correct system of inequalities from a graph?

Back

Look for the boundary lines and their slopes, then determine the direction of shading to match the inequalities.

Front

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

Back

The intersection represents the solution set where all inequalities are satisfied.

Front

What does the inequality x ≥ 2 indicate on a graph?

Back

It indicates a vertical line at x = 2, with the region to the right of the line shaded, including the line itself.