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 graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and find the region where the solutions overlap.

Front

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

Back

A point is a solution if it satisfies all inequalities in the system.

Front

What is the difference between a solution and a feasible region?

Back

A solution is a specific point that satisfies the inequalities, while the feasible region is the area on the graph where all solutions lie.

Front

What does it mean if a system of inequalities has no solution?

Back

It means there is no point that satisfies all inequalities simultaneously.

Front

What is the significance of the boundary line in a graph of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false.

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 and check if all inequalities are satisfied.

Front

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

Back

It means there are an infinite number of points that satisfy all inequalities in the system.

Front

What is the graphical representation of y > 2x - 4?

Back

A dashed line for y = 2x - 4, with the area above the line shaded.

Front

What is the graphical representation of y ≤ 2x - 1?

Back

A solid line for y = 2x - 1, with the area below the line shaded.