Systems of Linear Equations

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 two lines to intersect?

Back

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

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What are parallel lines?

Back

Lines that never intersect and have the same slope.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

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

Back

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

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

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

Back

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