Solving 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

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use dashed lines for 'greater than' or 'less than' and solid lines for 'greater than or equal to' or 'less than or equal to'. The solution set is where the shaded regions overlap.

Front

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

Back

A point is a solution of a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

How do you rewrite an inequality in 'y=' form?

Back

To rewrite an inequality in 'y=' form, isolate y on one side of the inequality. For example, from 3x - 6y > 12, you would rearrange it to y < (1/2)x - 2.

Front

What is the difference between 'y > mx + b' and 'y < mx + b'?

Back

'y > mx + b' represents the region above the line, while 'y < mx + b' represents the region below the line.

Front

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

Back

The solution set represents all possible solutions that satisfy all inequalities in the system, typically visualized as a shaded region on a graph.

Front

What is the significance of dashed and solid lines in graphing inequalities?

Back

Dashed lines indicate that points on the line are not included in the solution (for 'greater than' or 'less than'), while solid lines indicate that points on the line are included (for 'greater than or equal to' or 'less than or equal to').

Front

How can you determine if a point is part of the solution set?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What does the inequality 'y > 2' represent graphically?

Back

The inequality 'y > 2' represents all points above the horizontal line y = 2, not including the line itself.

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality separately on the same coordinate plane.