System of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

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

Back

If the slopes of the lines are the same but the y-intercepts are different, the system has no solution.

Front

How can you determine if a system of equations has one solution?

Back

If the slopes of the lines are different, the system has one solution.

Front

How can you determine if a system of equations has infinite solutions?

Back

If the equations are equivalent, meaning they represent the same line, the system has infinite solutions.

Front

Solve the system of equations: 2x - y = 4 and y = -2x + 8. What is the value of x?

Back

x = 3

Front

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

Back

Two lines that intersect at a single point.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that never intersect.