Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

How do you determine the number of solutions in a system of inequalities?

Back

By analyzing the graphs of the inequalities; they can intersect at one point, not intersect at all, or overlap infinitely.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

It means that the shaded regions of the inequalities overlap completely.

Front

How do you rewrite an inequality in 'y=' form?

Back

Isolate y on one side of the inequality.

Front

What is the significance of the inequality symbol in graphing?

Back

It determines whether the boundary line is solid (inclusive) or dashed (exclusive).

Front

What does the inequality y > 2 represent on a graph?

Back

It represents all points above the horizontal line y = 2, not including the line itself.

Front

How do you test 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.

Front

What is the difference between 'y ≤ 2' and 'y < 2'?

Back

'y ≤ 2' includes the line y = 2, while 'y < 2' does not.

Front

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

Back

It is a dashed line with a slope of 1/2, shaded below the line.

Front

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

Back

Graph each inequality on the same coordinate plane.