Systems of equations graphically

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 one solution?

Back

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

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

The graphs of the equations are the same line, overlapping each other.

Front

How can you find the solution to a system of equations graphically?

Back

By graphing the equations and identifying the point(s) where they intersect.

Front

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

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never meet.

Front

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

Back

Two lines that lie on top of each other.

Front

If the equations are y = 2x + 3 and y = 2x - 1, what is the solution?

Back

No solution (the lines are parallel).

Front

If the equations are y = x + 2 and y = -x + 4, what is the solution?

Back

(1, 3) (the lines intersect at this point).