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:
![\begin{cases} 6p+m=9\\4p+2m=8\end{cases}](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%206p%2Bm%3D9%5C%5C4p%2B2m%3D8%5Cend%7Bcases%7D%20)
Now, if you multiply the first equation by 2, the system becomes
![\begin{cases} 12p+2m=18\\4p+2m=8\end{cases}](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%2012p%2B2m%3D18%5C%5C4p%2B2m%3D8%5Cend%7Bcases%7D%20)
Subtract the second equation from the first:
![12p+2m - (4p+2m) = 18-8 \iff 8p = 10 \iff p = \dfrac{10}{8} = 1.25](https://tex.z-dn.net/?f=%2012p%2B2m%20-%20%284p%2B2m%29%20%3D%2018-8%20%5Ciff%208p%20%3D%2010%20%5Ciff%20p%20%3D%20%5Cdfrac%7B10%7D%7B8%7D%20%3D%201.25%20)
Plug this value into the first equation to get
![6p+m=9 \iff 6\cdot 1.25 +m = 9 \iff 7.5 +m=9 \iff m = 9-7.5 = 1.5](https://tex.z-dn.net/?f=%206p%2Bm%3D9%20%5Ciff%206%5Ccdot%201.25%20%2Bm%20%3D%209%20%5Ciff%207.5%20%2Bm%3D9%20%5Ciff%20m%20%3D%209-7.5%20%3D%201.5%20)
Answer:
<em>For part one...</em>
<em><u>you will multiply 4.5 by 3 to get 13.5 . </u></em>
<em>For part two,</em>
<u><em> you will multiply 3m by 4 to get 12.</em></u>
<u><em></em></u>
<em> (: </em><em><u>I hope this helps! BRAINLIEST is appreciated to get to virtuoso</u></em><em> :)</em>