Solving Systems by Graphing

Front

What is the solution to the system of equations represented by the point where the graphs intersect?

Back

The solution is the ordered pair where the two graphs cross, indicating the values that satisfy both equations.

Front

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

Back

The graph consists of parallel lines that never intersect.

Front

What is an ordered pair in the context of solving systems of equations?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the graph, indicating the solution to the system.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the definition of a system of equations?

Back

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

Front

How do you determine the solution to a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

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

Back

The intersection point represents the solution to the system, where both equations are satisfied.

Front

If two lines intersect at a single point, what does that indicate about the system of equations?

Back

It indicates that the system has one unique solution.

Front

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

Back

The graph shows two lines that intersect at exactly one point.

Front

What does it mean for two lines to be skew in the context of systems of equations?

Back

Skew lines are lines that do not intersect and are not parallel, typically found in three-dimensional space.