A1 Unit 6 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 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 does it mean for an inequality to be 'greater than' or 'less than'?

Back

'Greater than' (>) means that the value on the left is larger than the value on the right. 'Less than' (<) means the value on the left is smaller than the value on the right.

Front

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

Back

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

Front

What does shading above or below a line in a graph represent?

Back

Shading above a line represents all the points that satisfy the inequality where y is greater than the line. Shading below represents all points where y is less than the line.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid or dashed). 2. Choose a test point not on the line to determine which side to shade. 3. Shade the appropriate region.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap on the graph.

Front

What does the inequality y ≤ x + 4 represent graphically?

Back

It represents all points below or on the line y = x + 4, including the line itself.

Front

How can you check if an ordered pair is a solution to a system of inequalities?

Back

Substitute the x and y values of the ordered pair into each inequality. If both inequalities are true, then the ordered pair is a solution.

Front

What is the significance of the intersection of two shaded regions in a graph of inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities in the system.