7.279. $\left\{\begin{array}{l}x^{y^{2}-7 y+10}=1, \\ x+y=8\end{array},(x>0)\right.$.

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7.279. $\left\{\begin{array}{l}x^{y^{2}-7 y+10}=1, \\ x+y=8\end{array},(x>0)\right.$.
## Solution.

Let's write the given system of equations as $\left\{\begin{array}{l}x^{y^{2}-7 y+10}=x^{0} \\ x+y=8 .\end{array}\right.$, This system of equations is equivalent to two systems:

1) $\left\{\begin{array}{l}x=1 \\ x+y=8\end{array} \Leftrightarrow\left\{\begin{array}{l}x=1 \\ y=7\end{array}\right.\right.$
2) $\left\{\begin{array}{l}y^{2}-7 y+10=0, \\ x+y=8\end{array} \Leftrightarrow\left\{\begin{array}{l}x=6, \\ y=2,\end{array}\right.\right.$ or $\left\{\begin{array}{l}x=3, \\ y=5 .\end{array}\right.$

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0459.jpg?height=129&width=604&top_left_y=337&top_left_x=138)

Answer: $(1 ; 7),(6 ; 2),(3 ; 5)$.