Solving 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 if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you solve a system of equations graphically?

Back

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

Front

What is the substitution method for 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 for 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.

Front

How do you determine if two lines are parallel?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.