Systems of Equations by Inspection and Graphing

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 infinitely many solutions?

Back

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

Front

How can you solve a system of equations by inspection?

Back

By substituting values to see if they satisfy both equations.

Front

How can you solve a system of equations by graphing?

Back

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

Front

What is the solution to the system y = 5x - 2 and y = 2x - 5?

Back

(1, 3) - This system has 1 solution.

Front

What is the solution to the system y = 2x + 5 and y = 2x - 3?

Back

No solution - The lines are parallel.

Front

What is the solution to the system y = 4x + 5 and -4x + y = 5?

Back

Infinitely many solutions - The equations represent the same line.

Front

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

Back

Two parallel lines that never intersect.