If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. but if you buy four pens and two mechanical pencils, you'll get $2 change. how much does each pen and each pencil cost?

Let p be the prize of a pen and m the prize of a mechanical pencils. If you buy six pens and one mechanical pencil, you spend 6p+m. We know that this equals 9, because you get 1$ change from a 10$ bill.

Similarly, if you buy four pens and two mechanical pencils, you spend 4p+2m, which is 8$, because now you get a $2 change. Put these equation together in a system:

Now, if you multiply the first equation by 2, the system becomes

Subtract the second equation from the first:

Plug this value into the first equation to get

i dont get it. where are the "descriptions"?