Solving Systems by Graphing

Front

What is the solution to a system of equations when graphed?

Back

The solution is the point where the two lines intersect.

Front

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

Back

The (x,y) coordinates must satisfy both equations.

Front

What does it mean for two lines to intersect on a graph?

Back

It means they have a common solution, which is the point of intersection.

Front

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

Back

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

Front

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

Back

It means the lines are parallel and do not intersect.

Front

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

Back

It means the lines are coincident, lying on top of each other.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations, typically as lines on a coordinate plane.

Front

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

Back

It represents the values of x and y that satisfy both equations.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

What does it mean for a solution to be 'true' in the context of systems of equations?

Back

It means that the ordered pair satisfies both equations in the system.