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 if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

How can you solve a system of linear equations by graphing?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the elimination method in solving systems of linear equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method in solving systems of linear equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line where m is the slope and b is the y-intercept.

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 is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).