Graphing 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 it mean if an inequality is represented with a solid line?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is ≤ or ≥.

Front

What does it mean if an inequality is represented with a dashed line?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is < or >.

Front

How can 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 significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the inequality or system of inequalities.

Front

What does the inequality y > -1/5x - 1/2 represent graphically?

Back

It represents the area above the line y = -1/5x - 1/2, not including the line itself.

Front

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

Back

It represents the area below the line y = -2x - 4, including the line itself.

Front

What is the solution to the system of inequalities y > -1/5x - 1/2 and y ≤ -2x - 4?

Back

The solution is the region where the area above the line y = -1/5x - 1/2 overlaps with the area below the line y = -2x - 4.

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It divides the coordinate plane into two regions.