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 region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Rewrite the inequality in slope-intercept form (y = mx + b). 2. Graph the boundary line (solid for ≥ or ≤, dashed for > or <). 3. Shade the appropriate region (above or below the line).

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

Front

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

Back

'>' means 'greater than'. It indicates that the value must be strictly greater than a certain number.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the value can be less than or equal to a certain number.

Front

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

Back

'<' means 'less than'. It indicates that the value must be strictly less than a certain number.

Front

How do you determine which side to shade when graphing an inequality?

Back

To determine which side to shade, pick a test point (often (0,0)). If the point satisfies the inequality, shade the side that includes the point; otherwise, shade the opposite side.

Front

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

Back

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

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities in the system overlap. It represents all possible solutions.

Front

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

Back

A point is a solution if it satisfies all inequalities in the system. Substitute the point's coordinates into each inequality to check.