Graphing Systems of Equations

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 two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and never intersect.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts.

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 y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

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

Back

They determine the slope and y-intercept of the line.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.