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 for a system of equations to have one solution?

Back

It means that the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the graphs of the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, so they intersect at every point on that line.

Front

How can you determine if a system of equations has no solution?

Back

If the equations are parallel, they will have the same slope but different y-intercepts.

Front

What is the graphical representation of intersecting lines?

Back

Intersecting lines represent a system with one solution, where the lines cross at a single point.

Front

What is the graphical representation of parallel lines?

Back

Parallel lines represent a system with no solution, as they never meet.

Front

What is the graphical representation of the same line?

Back

The same line represents a system with infinitely many solutions, as every point on the line is a solution.

Front

How do you solve a system of equations by elimination?

Back

You can eliminate one variable by adding or subtracting the equations to isolate the other variable.

Front

What is the purpose of substitution in solving linear systems?

Back

Substitution allows you to solve one equation for a variable and then substitute that expression into the other equation.