12-19 Algebra 2 Warm-Up

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 on the same coordinate plane. Use a dashed line for < and >, and a solid line for ≤ and ≥. The solution is the overlapping shaded region.

Front

What does the inequality y ≥ -x - 1 represent graphically?

Back

It represents the region above and including the line y = -x - 1.

Front

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

Back

It represents the region below the line y = x + 4, not including the line itself.

Front

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the system of inequalities.

Front

What does it mean if a point lies on a dashed line in a graph of inequalities?

Back

It means that the point is not included in the solution set for inequalities that use < or >.

Front

What does it mean if a point lies on a solid line in a graph of inequalities?

Back

It means that the point is included in the solution set for inequalities that use ≤ or ≥.

Front

How can you tell if a point is a solution to the inequality y > -x - 1?

Back

If the y-coordinate of the point is greater than the value of -x - 1 when substituted into the inequality, then it is a solution.

Front

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

Back

The first step is to graph each inequality separately on the same coordinate plane.