Review System of Equations (E-Learning 1/6)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations intersect at exactly one point.

Front

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

Back

It means the equations represent the same line, overlapping each other.

Front

Solve the system by elimination: 5x + 8y = -12 and 3x + 5y = -7.

Back

(-4, 1)

Front

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are equal.

Front

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

Back

Two lines intersecting at a single point.

Front

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

Back

Two parallel lines that do not intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two overlapping lines that are the same.

Front

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

Back

If the equations simplify to a false statement, like 0 = 5.