B3. Solve the system of equations:

$$
\begin{aligned}
2 \log _{3} x-\log _{3} y & =2-\log _{3} 2 \\
0.2^{\sqrt{2 x-y-2.5}} & =1
\end{aligned}
$$

## 16th Knowledge Competition

 in mathematics for students of secondary technical and vocational schoolsNational Competition, April 16, 2016

## Problems for 4th Year

Time for solving: 120 minutes. In section A, we will award three points for each correct answer, and deduct one point for each incorrect answer. Enter the answers for section A in the left table, leave the right table blank.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-14.jpg?height=163&width=319&top_left_y=661&top_left_x=640)

| B1 | B2 | B3 |
| :--- | :--- | :--- |
|  |  |  |
B3.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-23.jpg?height=71&width=1736&top_left_y=2163&top_left_x=177)

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-23.jpg?height=69&width=1736&top_left_y=2230&top_left_x=177)

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-23.jpg?height=57&width=1739&top_left_y=2287&top_left_x=176)

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-23.jpg?height=54&width=1736&top_left_y=2343&top_left_x=177)

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-23.jpg?height=51&width=1736&top_left_y=2390&top_left_x=177)

Reduction to the quadratic equation $4 x^{2}-36 x+45=0$....................................................................................

Recording the solutions of the system of equations $x_{1}=\frac{15}{2}, y_{1}=\frac{25}{2}$ and $x_{2}=\frac{3}{2}, y_{2}=\frac{1}{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots 1+1$ point

## Fourth Year

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-24.jpg?height=143&width=234&top_left_y=357&top_left_x=928)