Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear 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 linear inequalities?

Back

To graph a system of linear 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 is where the shaded regions overlap.

Front

What does the solution to a system of linear inequalities represent?

Back

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

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

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

Back

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

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, 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 graphical representation of the inequality y < 2x - 1?

Back

The graphical representation is a dashed line for the equation y = 2x - 1, with the area below the line shaded.

Front

What does the inequality y ≥ -2x + 3 represent graphically?

Back

It represents a solid line for the equation y = -2x + 3, with the area above the line shaded.

Front

Which of the following points is a solution to the system: y ≤ 2x - 1 and y > -2x + 3? (0, 0), (1, 1), (-4, -2), (4, -2)

Back

(-4, -2) is a solution.

Front

Which of the following points is NOT a solution to the system: y ≤ 2x - 1 and y > -2x + 3? (0, 0), (3, -2), (3, -4), (4, -4)

Back

(0, 0) is NOT a solution.