I'm stuck. Can somebody help me solve this problem. The sum of our present ages is $41$. If I live $17$ more years, after doubling my present age, I will be $9$ years less than your present age. What are our present age?

$y=\text{Your age, and }x=\text{Mine}$.
$$x+y=41\\
\text{And also }17+2x=y-9\\
\implies 2x-y=-26$$
Let me do this a bit differently - probably not meant for precalculus, but here it goes anyway.
$$\begin{pmatrix}1&1\\2&-1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}41\\-26\end{pmatrix}$$
Then,
$$\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\dfrac{1}{3}&\dfrac{1}{3}\\ \dfrac{2}{3}&-\dfrac{1}{3}\end{pmatrix}\begin{pmatrix}41\\-26\end{pmatrix}\\
\implies \begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}5\\26\end{pmatrix}$$
