Pretest: Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean if a linear system has infinitely many solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

How can you determine if a linear system has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system with one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean to eliminate a variable in a system of equations?

Back

To eliminate a variable means to manipulate the equations so that one variable is removed, making it easier to solve for the other.

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for easier solving.

Front

What does it mean if two equations are dependent?

Back

Dependent equations are those that represent the same line, resulting in infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

Independent equations are those that represent different lines, resulting in either one solution or no solution.

Front

How do you identify parallel lines in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts.