Writing and Solving Systems of Equations in Story Problems

This video tutorial explains how to solve story problems by writing systems of equations. It covers the basics of systems of equations, including the need for as many equations as there are variables, and the three possible outcomes when solving them. The tutorial also describes three methods for solving systems: graphing, substitution, and elimination. It emphasizes the importance of defining variables and writing equations based on given constraints, using a story problem involving burgers and fries as an example. The video concludes with a discussion on additional constraints, such as non-negative values for variables.

What is one possible outcome when solving a system of two equations with two unknowns?

• The equations have no solutions.

• The equations have exactly two solutions.

• The equations have a solution that is a curve.

• The equations have a solution that is a circle.

Which method involves finding the point where two lines intersect?

• Elimination

• Graphing

• Integration

• Substitution

What is the first step in solving a story problem using a system of equations?

• Substitute values into equations

• Determine relationships and define variables

• Graph the equations

• Eliminate one variable

In the burger and fries example, what does the variable X represent?

• The total calories

• The number of burgers

• The cost of fries

• The number of fries

Why must X and Y be greater than or equal to zero in the burger and fries example?

• Because negative values are not allowed in equations

• Because you cannot order negative quantities

• Because the cost cannot be negative

• Because calories cannot be negative