Solving 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 has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How can you determine if a system of equations has no solution?

Back

If the slopes of the lines are equal but the y-intercepts are different.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line.

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution.