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 as if it were an equation. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

'>' means 'greater than'. It indicates that the value on the left is strictly greater than the value on the right.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all ordered pairs (x, y) that satisfy all inequalities in the system.

Front

How can 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 is the significance of the boundary line in graphing inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is '≤' or '≥', the line is solid; if it is '<' or '>', the line is dashed.

Front

What does it mean if a point lies above a boundary line in a graph of an inequality?

Back

If a point lies above a boundary line, it means that the point satisfies the inequality that corresponds to that line.

Front

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

Back

'y < mx + b' represents a region above a dashed line, while 'y ≤ mx + b' represents a region above a solid line, including the line itself.

Front

How do you find the intersection of two inequalities?

Back

The intersection of two inequalities is found by graphing both inequalities and identifying the region where their shaded areas overlap.