Systems 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 set of all points that satisfy all inequalities in the system.

Tags

CCSS.8.EE.C.8B

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 set is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality y ≤ x - 3 represent?

Back

It represents all points (x, y) that are below or on the line y = x - 3.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of the inequalities y ≥ -2 and y ≤ x - 3?

Back

The solution set includes all points that are above the line y = -2 and below or on the line y = x - 3.

Tags

CCSS.HSA.REI.D.12

Front

What does the symbol '≥' mean in inequalities?

Back

It means 'greater than or equal to'.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '≤' mean in inequalities?

Back

It means 'less than or equal to'.

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 a solution.

Front

What is the significance of the boundary line in a graph of an inequality?

Back

The boundary line separates the solution set from the non-solution set. Points on the line are included if the inequality is ≤ or ≥.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality y > -2x + 3 represent?

Back

It represents all points (x, y) that are above the line y = -2x + 3.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of the inequality y < 3x?

Back

It is a dashed line for y = 3x, with the area below the line shaded.

Tags

CCSS.HSA.REI.D.12