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 intersect at exactly one point.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

Front

In the equation y = mx + b, what does 'm' represent?

Back

The slope of the line.

Front

In the equation y = mx + b, what does 'b' represent?

Back

The y-intercept of the line.

Front

How can you determine if two lines are parallel?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.