Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are graphed on the same coordinate plane.

Front

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

Back

Substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

How do you graph the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 as a dashed line and shade above the line.

Front

What is the solution set of the inequality 5 ≥ x?

Back

The solution set includes all values of x that are less than or equal to 5.

Front

What is the significance of the inequality symbol in graphing?

Back

The inequality symbol determines whether the line is solid or dashed and indicates the direction of shading.

Front

How can you check if (2, 3) is a solution to the system -4y < 8 and 6x + 3 > 1?

Back

Substitute x=2 and y=3 into both inequalities. It satisfies both, so it is a solution.

Front

What does the term 'feasible region' refer to in graphing systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.

Front

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

Back

Graph each inequality as if it were an equation to find the boundary lines.