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 region where the graphs of the inequalities overlap.

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.

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.

Front

How do you represent a solution to a system of inequalities graphically?

Back

The solution is represented by shading the region where the graphs of the inequalities overlap.

Front

What type of line is used for inequalities with '≤' or '≥'?

Back

A solid line is used for inequalities with '≤' or '≥' to indicate that points on the line are included in the solution.

Front

What type of line is used for inequalities with '<' or '>'?

Back

A dotted line is used for inequalities with '<' or '>' to indicate that points on the line are not included in the solution.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Shade the appropriate region for each inequality. 3. The solution is where the shaded regions overlap.

Front

What does the inequality 'y > 3' represent graphically?

Back

It represents all points above the horizontal line y = 3, not including the line itself.

Front

What does the inequality 'y ≥ 3' represent graphically?

Back

It represents all points on or above the horizontal line y = 3, including the line itself.

Front

If a system of inequalities has no overlapping shaded region, what does that mean?

Back

It means there is no solution to the system of inequalities.