Solving Systems of Two Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean if a system of linear equations has a unique solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are coincident, meaning they lie on top of each other.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

How can you determine if two lines are coincident?

Back

If they have the same slope and the same y-intercept.

Front

What is the graphical representation of a unique solution?

Back

Two lines intersecting at one point.

Front

What is the graphical representation of no solution?

Back

Two parallel lines that never meet.

Front

What is the graphical representation of infinitely many solutions?

Back

Two lines that overlap completely (coincident lines).

Front

If the equations are y = 2x + 3 and 2y = 4x + 6, what type of solution do they represent?

Back

Infinitely many solutions (coincident lines).