Graphing Systems of Equations

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 a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines coincide, or are the same line.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the intersection point.

Front

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

Back

(1, 3)

Front

What is the slope of the line represented by the equation y = 3x - 5?

Back

3

Front

What is the y-intercept of the line represented by the equation y = -2x + 6?

Back

6

Front

If two lines have the same slope but different y-intercepts, what can be said about the system of equations?

Back

The system has no solution.

Front

What is the graphical representation of the solution (2, -3)?

Back

It is the point where x = 2 and y = -3 on the graph.