Graphing Systems of Inequalities

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 ordered pairs that satisfy all inequalities in the system.

Front

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

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system when substituted into them.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation (using a solid line for ≤ or ≥ and a dashed line for < or >). 2. Shade the region that satisfies the inequality. 3. The solution to the system is where the shaded regions overlap.

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 does the inequality y > -1/5x - 1/2 represent graphically?

Back

It represents the region above the line y = -1/5x - 1/2, not including the line itself.

Front

What does the inequality y ≤ -2x - 4 represent graphically?

Back

It represents the region below the line y = -2x - 4, including the line itself.

Front

How can 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 the point satisfies all inequalities, it is a solution.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.

Front

What does it mean for a point to be 'not a solution' to a system of inequalities?

Back

It means that the point does not satisfy at least one of the inequalities in the system when substituted into them.