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 solve the inequality y - 4 > 12?

Back

Add 4 to both sides: y > 16.

Front

What does the graph of y < -2x + 1 look like?

Back

It is a region below the line y = -2x + 1, with a dashed line indicating that points on the line are not included.

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤).

Front

What does a dashed line indicate in graphing inequalities?

Back

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

Front

How do you represent the inequality x > -3 on a number line?

Back

Draw an open circle at -3 and shade to the right.

Front

What is the solution to the system of inequalities y > 2x + 1 and y < -x + 4?

Back

The solution is the region where both inequalities overlap on the graph.

Front

What is the first step in solving a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane.

Front

What does the inequality y ≤ 2x + 1 represent?

Back

It represents all points on or below the line y = 2x + 1.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.