Flashcard 8H.2.5 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

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

How do you graph the inequality y > -x - 1?

Back

To graph y > -x - 1, first graph the line y = -x - 1 using a dotted line (since it's a strict inequality). Then shade the area above the line.

Front

What is the solution set of the system y > -x - 1 and y ≥ x + 4?

Back

The solution set includes all points that lie above the line y = -x - 1 and on or above the line y = x + 4.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What type of line is used when graphing y < x + 4?

Back

A dotted line is used when graphing y < x + 4 because the inequality is strict (does not include equality).

Front

What does the solution (0,0) indicate for the system y > -x - 1 and y ≥ x + 4?

Back

The point (0,0) is a solution to the system because it satisfies both inequalities.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dotted line indicates that the points on the line are not included (>, <).

Front

How do you identify the correct graph for an inequality?

Back

To identify the correct graph for an inequality, determine the boundary line and whether to shade above or below the line based on the inequality symbol.