Systems of Linear Inequalities

Front

What symbols indicate a solid line when graphing an inequality?

Back

≤, ≥

Front

Which of the following is a solution to the system of inequalities: (0, -2), (-3, 0), (-3, 2), (1, 1)?

Back

(1, 1)

Front

Which of the following is a solution to the system of inequalities: (0, 0), (-3, 0), (2, -5), (3, -1)?

Back

(2, -5)

Front

What is a linear inequality?

Back

An inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

Front

What does the solution set of a system of linear inequalities represent?

Back

The set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for ≤ or ≥ and a dashed line for < or >. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

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

Back

Graph each inequality on the same coordinate plane.

Front

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

Back

It means that the point satisfies all inequalities in the system.

Front

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

Back

Substitute the point's coordinates into each inequality to see if they hold true.