Solving Systems of Equations 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

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

Back

You graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What does it mean if two lines intersect at a point?

Back

The coordinates of the intersection point are the solution to the system of equations.

Front

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect, indicating the system has no solution.

Front

What does it mean if two lines are the same?

Back

They overlap completely, indicating the system has infinite solutions.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How can you tell if a system of equations has no solution by looking at the graphs?

Back

If the lines are parallel, the system has no solution.

Front

How can you tell if a system of equations has infinite solutions by looking at the graphs?

Back

If the lines are the same, the system has infinite solutions.