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Team $X$ scored $p$ points more than team $Y$, and the two teams together scored a total of 10 points.
Compare:
Column A: Twice the number of points team $Y$ scored
Column B: $10 - p$
Let team $Y$'s score $= y$. Then team $X$'s score $= y + p$.
Together: $y + (y + p) = 10 \Rightarrow 2y + p = 10 \Rightarrow 2y = 10 - p$.
Column A $= 2y = 10 - p$ = Column B.
The two quantities are equal.
The product of upper-triangular matrices $\begin{pmatrix}1&k\\0&1\end{pmatrix}$ gives $\begin{pmatrix}1&\sum k\\0&1\end{pmatrix}$.
$\sum_{k=1}^{n-1}k = \dfrac{(n-1)n}{2} = 78 \Rightarrow n(n-1)=156 \Rightarrow n=13$
The inverse of $\begin{pmatrix}1&n\\0&1\end{pmatrix} = \begin{pmatrix}1&13\\0&1\end{pmatrix}$ is $\begin{pmatrix}1&-13\\0&1\end{pmatrix}$.
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