Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which are the points that satisfy the inequality.

Front

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

Back

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

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set of a system of linear inequalities is the region where the graphs of the inequalities overlap, representing all the points that satisfy all inequalities in the system.

Front

What does the symbol '>' mean in a linear inequality?

Back

The symbol '>' means that the value on the left side of the inequality is greater than the value on the right side.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means that the value on the left side of the inequality is less than or equal to the value on the right side.

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Back

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality by providing a starting point.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the line is solid (≤ or ≥) and not included if the line is dotted (< or >).