Systems of Equations Applications

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

Front

How do you represent a system of equations graphically?

Back

By plotting the equations on a coordinate plane and observing their 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 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, making it easier to solve for the other.

Front

What is the context of the solution (90,60) in the ticket sales problem?

Back

There were 90 adult tickets and 60 child tickets sold.

Front

How do you set up a system of equations from a word problem?

Back

Identify the variables, write equations based on the relationships described, and include any constraints.

Front

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

Back

They represent the rate of change or the relationship between the variables in the equations.