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

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping completely.

Front

How do you graph a system of equations?

Back

Plot each equation on the same coordinate plane and look for points of intersection.

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 - 2?

Back

3

Front

What is the y-intercept of the equation y = -2x + 5?

Back

5

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

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

Back

The point(s) where the graphs of the equations intersect.