Solving 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 to the system is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. 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 region that satisfies the inequality.

Front

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

Back

A point is a solution of a system of linear inequalities if it satisfies all inequalities in the system. This means that when the coordinates of the point are substituted into each inequality, the resulting statements are true.

Front

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

Back

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

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

Front

What is the significance of the shaded region in the graph of a system of inequalities?

Back

The shaded region represents all possible solutions to the system of inequalities. Any point within this region satisfies all inequalities in the system.

Front

What is the graphical representation of the inequality y > 2x - 3?

Back

The graphical representation is a dashed line for the equation y = 2x - 3, with the region above the line shaded, indicating that y must be greater than the values on the line.

Front

How do you find the intersection of two linear inequalities?

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To find the intersection, graph both inequalities on the same coordinate plane and identify the region where the shaded areas overlap. This overlapping region represents the solution set for the system.

Front

What does the inequality y < 2x + 1 represent graphically?

Back

Graphically, it represents a dashed line for the equation y = 2x + 1, with the region below the line shaded, indicating that y must be less than the values on the line.

Front

What is the role of the boundary line in a system of linear inequalities?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. It is crucial for determining the solution set.