Solve Systems by 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 a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What does the graph of a system of equations with one solution look like?

Back

Two lines that intersect at a single point.

Front

What does the graph of a system of equations with no solution look like?

Back

Two parallel lines that never intersect.

Front

What does the graph of a system of equations with infinitely many solutions look like?

Back

Two lines that lie on top of each other (coincident lines).

Front

How do you find the solution to a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate where the line crosses the y-axis.

Front

How can you determine if two lines are parallel from their equations?

Back

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