Solving Systems of Equations by Graphing

Front

What does the graph of a system of equations with no solution look like?

Back

Parallel lines.

Front

Where do the lines intersect in a system of equations?

Back

The point or points where they intersect.

Front

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

Back

The lines are parallel and never intersect.

Front

What is the solution to a system of equations?

Back

The point or points where the lines intersect, which can be a single point, infinitely many points, or no points.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3).

Front

If two lines intersect at one point, how many solutions does the system have?

Back

One solution.

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel, existing in different planes.

Front

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

Back

The equations represent the same line.

Front

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

Back

Two lines that intersect at a single point.

Front

What is the significance of the intersection point in a system of equations?

Back

It represents the values of the variables that satisfy both equations.