Solving Systems of Inequalities

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 ordered pairs that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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 inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ or ≥). Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution to a system of inequalities represent?

Back

The solution to a system of inequalities represents all the points (x, y) that satisfy all the inequalities in the system, typically visualized as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line and has an equality sign (e.g., y = mx + b), while a linear inequality represents a region of the graph and includes inequality signs (e.g., y < mx + b or y ≥ mx + b).

Front

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

Back

To determine if a point is a solution to a system of inequalities, 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 significance of the boundary line in a graph of an inequality?

Back

The boundary line in a graph of an inequality indicates the limit of the solution set. If the inequality is strict (e.g., < or >), the line is dashed, meaning points on the line are not included in the solution. If the inequality is inclusive (e.g., ≤ or ≥), the line is solid, meaning points on the line are included.

Tags

CCSS.HSA.REI.D.12

Front

How do you rewrite an inequality in 'y=' form?

Back

To rewrite an inequality in 'y=' form, isolate y on one side of the inequality. This often involves rearranging the terms and simplifying the expression.

Front

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

Back

The graphical representation of the inequality y ≤ 2x - 1 is a solid line with a slope of 2 and a y-intercept of -1, with the region below the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A point is a solution of the system of inequalities if it lies within the shaded region of the graph that represents the solution set for all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

How do you find the feasible region in a system of inequalities?

Back

The feasible region in a system of inequalities is found by graphing all inequalities and identifying the area where the shaded regions overlap. This region contains all possible solutions.

Tags

CCSS.HSA.REI.D.12