TEST Solving Linear Systems & 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 (e.g., <, >, ≤, ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of the boundary line.

Front

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

Back

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

Front

How do you determine the boundary line for a linear inequality?

Back

To determine the boundary line, convert the inequality to an equation (replace the inequality symbol with an equals sign) and graph that line.

Front

What does the solution (1, -1) represent in a linear system?

Back

The solution (1, -1) represents the point where the two lines intersect, indicating the values of x and y that satisfy both equations.

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables that are solved together.

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What are the possible outcomes when solving a system of linear equations?

Back

The possible outcomes are: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines).

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What does it mean if a system of linear equations has no solutions?

Back

It means that the lines representing the equations are parallel and never intersect.

Front

How do you graph a linear inequality in two variables?

Back

1. Graph the boundary line. 2. Use a solid line for ≤ or ≥, and a dashed line for < or >. 3. Shade the appropriate region based on the inequality.

Front

What is the significance of the inequality symbol in a linear inequality?

Back

The inequality symbol indicates the relationship between the two expressions and determines whether the boundary line is solid or dashed.