toriginsberg
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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?

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 s class=

Respuesta :

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

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

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:

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

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.

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