Systems of equations and inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for an ordered pair to be a solution of a system of inequalities?

Back

It means that the ordered pair satisfies all inequalities in the system.

Front

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

Back

Substitute the x and y values of the point into each inequality. If all inequalities are satisfied, the point is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented by a shaded region on one side of the boundary line, which is dashed if the inequality is strict (< or >) and solid if it is inclusive (≤ or ≥).

Front

What does the shading in a graph of inequalities represent?

Back

The shading represents all the possible solutions that satisfy the inequality.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

How can you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Front

What does it mean for a region to be unbounded in the context of inequalities?

Back

An unbounded region extends infinitely in at least one direction and does not have a defined boundary.

Front

How do you identify which region to shade when given a system of inequalities?

Back

Test a point not on the boundary line (often (0,0) if it's not on the line) to see if it satisfies the inequality. Shade the region that includes the point if it satisfies the inequality.