System of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution set of a system of inequalities represent?

Back

The set of all points (x, y) that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than (not including the boundary), while '≥' means greater than or equal to (including the boundary).

Tags

CCSS.6.EE.B.8

Front

How can you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line divides the coordinate plane into two regions; one where the inequality holds true and one where it does not.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If the inequality is ≤ or ≥, the point is included in the solution set. If the inequality is < or >, the point is not included.

Tags

CCSS.HSA.REI.D.12

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints described in the problem, define variables, and translate the constraints into inequalities.

Front

What is the graphical representation of the solution to a system of inequalities?

Back

The solution is represented by the shaded region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

What is the role of test points in solving inequalities?

Back

Test points help determine which side of the boundary line satisfies the inequality.

Tags

CCSS.HSA.REI.D.12