Solving Systems of Equations by Graphing

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines representing the equations are the same, meaning they overlap completely.

Front

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

Back

The solution is the point where the two lines intersect on the graph.

Front

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

Back

The lines are parallel and never intersect.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = 2x - 3?

Back

There is no solution, as the lines are parallel.

Front

How do you verify if a point is a solution to a system of equations?

Back

Substitute the (x,y) coordinates into both equations; if both equations are satisfied, it is a solution.

Front

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

Back

It represents the solution to the system, where both equations are true.

Front

What does it mean if a system of equations has exactly one solution?

Back

The lines intersect at a single point, indicating a unique solution.

Front

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

Back

The solution is (1, 5), where the two lines intersect.

Front

What are the characteristics of a consistent system of equations?

Back

A consistent system has at least one solution, which can be either unique or infinitely many.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, typically represented by parallel lines.