Systems of Equations (Graphing)

Front

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

Back

The two lines are the same line.

Front

What is the solution to the system of equations represented by the lines y = x - 2 and y = 3x - 4?

Back

(1, -1)

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 5?

Back

(6, -2)

Front

What happens when you graph the same equation twice?

Back

You will have infinite solutions.

Front

Is (4, 1) a solution for the system of equations y = -x + 5 and y = 2x - 7?

Back

Yes.

Front

What are the characteristics of parallel lines in a system of equations?

Back

They have no solutions.

Front

What does it mean if two lines intersect at a single point?

Back

The system has one unique solution.

Front

How can you determine if a point is a solution to a system of equations?

Back

Plug the x and y values into both equations; if both are true, it's a solution.

Front

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

Back

Two parallel lines.

Front

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

Back

Two intersecting lines.