Systems of Inequalities Closure

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality. The solution is where the shaded regions overlap.

Front

What does it mean if a line is solid in a graph of inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is ≤ or ≥.

Front

What does it mean if a line is dashed in a graph of inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is < or >.

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the intersection of shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.

Front

What is the graphical representation of the inequality y < x - 2?

Back

The graph of y < x - 2 is a dashed line with a slope of 1 that crosses the y-axis at -2, with the area below the line shaded.

Front

What is the graphical representation of the inequality y ≥ 3?

Back

The graph of y ≥ 3 is a solid horizontal line at y = 3, with the area above the line shaded.

Front

How do you solve a system of inequalities algebraically?

Back

To solve a system of inequalities algebraically, isolate the variable in each inequality and find the range of values that satisfy all inequalities.

Front

What is the solution set of the system of inequalities y < -x + 2 and y > 3?

Back

The solution set is the region above the line y = 3 and below the line y = -x + 2, where the two regions overlap.