Flashcard review

Front

What is a system of equations?

Back

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

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and finding the point(s) where they intersect.

Front

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

Back

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

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.

Front

How do you graph an inequality?

Back

By shading the region of the graph that satisfies the inequality and using a dashed line for < or > and a solid line for ≤ or ≥.

Front

What is the solution to the inequality ½ ≤ x?

Back

x is any number greater than or equal to ½.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the relationship between the equations: no solution (parallel lines), one solution (intersecting lines), or infinitely many solutions (same line).

Front

What does it mean for a system to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the purpose of surveying people about preferences?

Back

To gather data and analyze trends or opinions on a specific topic.