11-09 Systems of Inequalities Flashcard

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 region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does it mean if a region is shaded in a graph of inequalities?

Back

Shaded regions indicate all the possible solutions to the inequality or system of inequalities.

Front

What is the difference between '≤' and '<'?

Back

'≤' means less than or equal to, including the boundary line, while '<' means less than, excluding the boundary line.

Front

What is the solution to the system of inequalities x + 3y < 9 and -2x + y ≥ 10?

Back

The solution is the region where both inequalities are satisfied, which can be found by graphing.

Front

What does the term 'feasible region' refer to in systems of inequalities?

Back

The feasible region is the area on a graph where all the constraints of the inequalities are satisfied.

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 linear inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What does it mean for a system of inequalities to be inconsistent?

Back

An inconsistent system has no solution, meaning the graphs of the inequalities do not intersect.

Front

What is the graphical representation of the inequality y > 2x + 1?

Back

The graph will have a dashed line for y = 2x + 1, and the region above the line will be shaded.