Question

Three friends: Alex, Maya and Kansas, all bought slices of pizza from the parlor. Alex bought 8 slices of pizza and 2 drinks, he spent a total of $24 ,Maya bought 12 slices of pizza and 3 drinks, He spent a total of $32. Calculate the cost of each item. When will Maya and Alex spend the same amount?

Answer 1

There is no solution to this system of equations; they will never spend the same amount.

The system of equations would be
$\left \{ {{8p+2d=24} \atop {12p+3d=32}} \right.$

We want one of the variables to have the same coefficient; we will make the coefficients of p be the same.  To accomplish this, we will multiply the top equation by 3 and the bottom equation by 2:

$\left \{ {{(3(8p+2d=24)} \atop {2(12p+3d=32)}} \right \\ \\ \left \{ {{24p+6d=72} \atop {24p+6d=64}} \right$

When we subtract the equations to cancel p, we also cancel d in the process, leaving us 

0 = 8

Since this is never true, there is no solution to the system.