Systems of Linear Equations - graphing

Front

What is a system of linear equations?

Back

A set of two or more linear 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 do you graph a linear equation?

Back

Identify the y-intercept and slope, then plot the y-intercept and use the slope to find another point.

Front

What is the slope-intercept form of a linear equation?

Back

Front

Back

The y-intercept is -4.

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; inconsistent if it has no solutions.

Front

What does it mean for a system to be dependent?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

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.