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 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 equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing the intersection points.

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 graphical method for solving systems of equations?

Back

Plotting the equations on a graph and finding the intersection point.

Front

If a system of equations is represented by y = mx + b, what do m and b represent?

Back

m is the slope of the line, and b is the y-intercept.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines on a graph.

Front

How do you represent a system of equations algebraically?

Back

By writing two or more equations that share the same variables.