10 years
1) Considering that we can call the age of a stamp by "s" and the age of a coin by "c" we can write out the following system of Linear Equations:
[tex]\begin{gathered} 2s+c=45 \\ 3s-c=5 \end{gathered}[/tex]Note that we can solve it using the Elimination Method.
2) So let's add simultaneously both equations:
[tex]\begin{gathered} 2s+c=45 \\ 3s-c=5 \\ -------- \\ 5s=50 \\ \frac{5s}{5}=\frac{50}{5} \\ s=10 \end{gathered}[/tex]We can plug into that s=10 and find the age of a coin as well:
[tex]\begin{gathered} 2(10)+c=45 \\ c=45-20 \\ c=20 \end{gathered}[/tex]Note that we subtracted 20 from both sides.
3) Hence, the age of a stamp is 10 years
