AA Unit 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

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, using solid lines for '≥' or '≤' and dashed lines for '>' or '<'. The solution is the overlapping shaded region.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line represents that the points on the line are included in the solution set, which is the case for inequalities with '≥' or '≤'.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which is the case for inequalities with '>' or '<'.

Front

What is the solution to the inequality y < 2x + 3?

Back

The solution is the region below the line y = 2x + 3, not including the line itself.

Front

How do you determine the shading direction for an inequality?

Back

To determine the shading direction, test a point not on the line (usually (0,0)). If the point satisfies the inequality, shade the region that includes that point.

Front

What is the graphical representation of the inequality x > -3?

Back

The graphical representation is a dashed vertical line at x = -3, with shading to the right of the line.

Front

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

Back

'y < mx + b' uses a dashed line and shades below the line, while 'y ≥ mx + b' uses a solid line and shades above the line.

Front

How can you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is solid or dashed, then find the direction of shading to establish the inequality.

Front

What does the solution set of a system of inequalities look like?

Back

The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap.