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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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 ≥.

Tags

CCSS.HSA.REI.D.12

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 >.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12