Intro to system of equations - graphs

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 graphs of the equations intersect at exactly one point.

Front

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

Back

It means the graphs of the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so they intersect at every point on that 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 point(s) where they intersect.

Front

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

Back

(1, 3)

Front

What is the solution to the system: y = 3x - 2 and y = 2x + 1?

Back

(3, 7)

Front

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

Back

If the lines are parallel, they will never intersect.

Front

How can you tell if a system of equations has infinite solutions?

Back

If the lines are the same, they will overlap completely.

Front

What is the graphical representation of the solution (1, -1)?

Back

It is the point where x = 1 and y = -1 on the graph.