Excel for Marketing Managers

Solving Systems of Equations

Solving
Systems of
Equations

cursor to the next cell that needs input. After the equations are entered, the

student needs to decide, by looking at the original equations, what number will

be used to multiply the first equation, and what number will multiply the

second. The student then enters the number that will divide both sides of the

equation to solve for x. Finally, the student must compare the equations at the

end of the worksheet with the originals to see if they match, ensuring that the

work was done correctly.

You need to decide if you will give the students problems that have a solution,

called simultaneous equations, or meet one of these two special circumstances:

If the two equations are parallel lines, the system is called inconsistent, and

will have no solution. As the students enter numbers, everything will appear

normal until they are asked to divide by the coefficient of x in Step 5 of the

worksheet. At this point, the x-coefficient is zero, and the answer cells will fill

with ####. However, upon examining what is displayed above, students will

notice that in Steps 3a and 3b, the calculations resulted in identical left sides

of the two equations, with different values on the right.

Another circumstance results in completely identical equations after doing

Steps 3a and 3b. This is when one equation is actually a multiple of the other,

and is called a dependent system. As in an inconsistent system, the final step

will result in #### being displayed. In this situation, however, instead of no

solution, there are an infinite number of solutions. It is up to the student to be

able to recognize the difference.

Excel Extras

With some expansion, this worksheet could also be used to solve a system of

three equations in three unknowns. However, since the focus of this book is for

the middle grades, that particular worksheet is outside the scope of this book.