Solutions for 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

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

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

Back

By finding the point where the lines intersect on the graph.

Front

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

Back

(1, 3)

Front

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

Back

No Solution.

Front

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

Back

(1, 1)

Front

What is the graphical representation of a system with infinite solutions?

Back

Two overlapping lines on the graph.

Front

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

Back

Two parallel lines on the graph.