be the cost of a doughnut and
the cost of a cupcake. He used the purchases he and Martha-Jon made to write the system of equations.
If Ron-Jon is right we should be able to solve this system. Let's solve it using the . First we will multiply Equation (I) by
as this will lead to the
-terms getting the same coefficient.
Now we have the following system.
We can see that Ron-Jon's system consists of two identical equations. This means that there exist infinitely many solutions. With infinitely many solutions there is no way to tell the exact cost of neither a doughnut nor a cupcake. Therefore, Martha-Jon is right.