System of Inequalities PRACTICE ASSIGNMENT

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

1. Graph each inequality as if it were an equation (using a solid line for ≤ or ≥ and a dashed line for < or >). 2. Shade the appropriate region for each inequality. 3. The solution is where the shaded regions overlap.

Front

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

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system.

Front

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

Back

Substitute the coordinates 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 a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥.

Front

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

Back

The symbol '>' indicates that the value on the left is greater than the value on the right, and does not include the boundary.

Front

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

Back

The symbol '<' indicates that the value on the left is less than the value on the right, and does not include the boundary.

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right, including the boundary.

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right, including the boundary.

Front

How do you solve a system of inequalities algebraically?

Back

1. Solve one inequality for one variable. 2. Substitute this expression into the other inequality. 3. Solve for the remaining variable.