Solving Systems of Equations Graphically

Front

What is a system of equations?

Back

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

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 where they meet.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point (x, y) where the lines representing the equations intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solution because they never intersect.

Front

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

Back

(1, 3) - The point where the two lines intersect.

Front

What does 'infinitely many solutions' mean in the context of systems of equations?

Back

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

Front

How can you determine if a system of equations has no solution graphically?

Back

If the lines are parallel and do not intersect.

Front

What is the significance of the ordered pair (x, y) in a system of equations?

Back

It represents the solution to the system, indicating the values of x and y that satisfy both equations.

Front

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

Back

Graph each equation on the same coordinate plane.

Front

What does it mean if the solution to a system of equations is (6, 3)?

Back

It means that when x = 6 and y = 3, both equations are satisfied.